Question 1

determine whether the recurrence relation is a linear homogeneous recurrence relation with constant coeﬃcients.
-$$a _ { n } = 5 a _ { n - 1 } ^ { 2 } - 3 a _ { n - 2 } ^ { 2 }$$

Accepted Answer

No

Question 2

Find the solution of the recurrence relation a_n = 3a_n−1 with a₀ = 2.

Accepted Answer

$$a _ { n } = 2 \cdot 3 ^ { n }$$

Question 3

determine whether the recurrence relation is a linear homogeneous recurrence relation with constant coeﬃcients.
-$$a _ { n } - 7 a _ { n - 2 } + a _ { n - 5 } = 0$$

Accepted Answer

Yes

Question 4

determine whether the recurrence relation is a linear homogeneous recurrence relation with constant coeﬃcients.
-$$a _ { n } = 0.7 a _ { n - 1 } - 0.3 a _ { n - 2 }$$

Accepted Answer

The answer of determine whether the recurrence relation is a...

Question 5

determine whether the recurrence relation is a linear homogeneous recurrence relation with constant coeﬃcients.
-$$a _ { n } = a _ { n - 3 }$$

Accepted Answer

The answer of determine whether the recurrence relation is a...

Question 6

describe each sequence recursively. Include initial conditions and assume that the sequences begin with aS1U1B11S1U1B0. -a_n = the number of bit strings of length n that begin with 1

Accepted Answer

The answer of describe each sequence recursively. Include initial conditions...

Question 7

determine whether the recurrence relation is a linear homogeneous recurrence relation with constant coeﬃcients.
-$$a _ { n } + a _ { n - 1 } = 1$$

Accepted Answer

The answer of determine whether the recurrence relation is a...

Question 8

solve the recurrence relation either by using the characteristic equation or by discovering a pattern formed by the terms.
-$$a _ { n } = 5 a _ { n - 1 } - 4 a _ { n - 2 } , \quad a _ { 0 } = 1 , a _ { 1 } = 0$$

Accepted Answer

The answer of solve the recurrence relation either by using...

Question 9

solve the recurrence relation either by using the characteristic equation or by discovering a pattern formed by the terms.
-$$a _ { n } = a _ { n - 2 } , \quad a _ { 0 } = 2 , a _ { 1 } = - 1$$

Accepted Answer

The answer of solve the recurrence relation either by using...

Question 10

solve the recurrence relation either by using the characteristic equation or by discovering a pattern formed by the terms.
-$$a _ { n } = 5 a _ { n - 1 } - 4 a _ { n - 2 } , \quad a _ { 0 } = 0 , a _ { 1 } = 1$$

Accepted Answer

The answer of solve the recurrence relation either by using...

Question 11

A vending machine dispensing books of stamps accepts only $1 coins, $1 bills, and $2 bills. Let an denote

Accepted Answer

The answer of A vending machine dispensing books of stamps...

Question 12

describe each sequence recursively. Include initial conditions and assume that the sequences begin with aS1U1B11S1U1B0. -a_n = the number of ways to go down an n-step staircase if you go down 1, 2, or 3 steps at a time

Accepted Answer

The answer of describe each sequence recursively. Include initial conditions...

Question 13

describe each sequence recursively. Include initial conditions and assume that the sequences begin with aS1U1B11S1U1B0. -a_n = the number of bit strings of length n that contain a pair of consecutive 0's

Accepted Answer

The answer of describe each sequence recursively. Include initial conditions...

Question 14

determine whether the recurrence relation is a linear homogeneous recurrence relation with constant coeﬃcients.
-$$a _ { n } = n a _ { n - 1 }$$

Accepted Answer

The answer of determine whether the recurrence relation is a...

Question 15

solve the recurrence relation either by using the characteristic equation or by discovering a pattern formed by the terms.
-$$a _ { n } = 2 a _ { n - 1 } + 5 , \quad a _ { 0 } = 3$$

Accepted Answer

The answer of solve the recurrence relation either by using...

Question 16

describe each sequence recursively. Include initial conditions and assume that the sequences begin with aS1U1B11S1U1B0. -a_n = the number of bit strings of length n with an even number of 0's

Accepted Answer

The answer of describe each sequence recursively. Include initial conditions...

Question 17

solve the recurrence relation either by using the characteristic equation or by discovering a pattern formed by the terms.
-$$a _ { n } = 2 a _ { n - 1 } + 2 a _ { n - 2 } , \quad a _ { 0 } = 0 , a _ { 1 } = 1$$

Accepted Answer

The answer of solve the recurrence relation either by using...

Question 18

solve the recurrence relation either by using the characteristic equation or by discovering a pattern formed by the terms.
-$$a _ { n } = 3 n a _ { n - 1 } , \quad a _ { 0 } = 2$$

Accepted Answer

The answer of solve the recurrence relation either by using...

Question 19

solve the recurrence relation either by using the characteristic equation or by discovering a pattern formed by the terms.
-$$a _ { n } = a _ { n - 1 } + 3 n , \quad a _ { 0 } = 5$$

Accepted Answer

The answer of solve the recurrence relation either by using...

Question 20

solve the recurrence relation either by using the characteristic equation or by discovering a pattern formed by the terms.
-$$a _ { n } = - 10 a _ { n - 1 } - 21 a _ { n - 2 } , \quad a _ { 0 } = 2 , a _ { 1 } = 1$$

Accepted Answer

The answer of solve the recurrence relation either by using...

Quiz 8: A: Advanced Counting Techniques

determine whether the recurrence relation is a linear homogeneous recurrence relation with constant coeﬃcients. - $a _ { n } = 5 a _ { n - 1 } ^ { 2 } - 3 a _ { n - 2 } ^ { 2 }$

Find the solution of the recurrence relation a_n = 3a_n−1 with a₀ = 2.

determine whether the recurrence relation is a linear homogeneous recurrence relation with constant coeﬃcients. - $a _ { n } - 7 a _ { n - 2 } + a _ { n - 5 } = 0$

determine whether the recurrence relation is a linear homogeneous recurrence relation with constant coeﬃcients. - $a _ { n } = 0.7 a _ { n - 1 } - 0.3 a _ { n - 2 }$

determine whether the recurrence relation is a linear homogeneous recurrence relation with constant coeﬃcients. - $a _ { n } = a _ { n - 3 }$

describe each sequence recursively. Include initial conditions and assume that the sequences begin with a₁. -a_n = the number of bit strings of length n that begin with 1

determine whether the recurrence relation is a linear homogeneous recurrence relation with constant coeﬃcients. - $a _ { n } + a _ { n - 1 } = 1$

solve the recurrence relation either by using the characteristic equation or by discovering a pattern formed by the terms. - $a _ { n } = 5 a _ { n - 1 } - 4 a _ { n - 2 } , \quad a _ { 0 } = 1 , a _ { 1 } = 0$

solve the recurrence relation either by using the characteristic equation or by discovering a pattern formed by the terms. - $a _ { n } = a _ { n - 2 } , \quad a _ { 0 } = 2 , a _ { 1 } = - 1$

solve the recurrence relation either by using the characteristic equation or by discovering a pattern formed by the terms. - $a _ { n } = 5 a _ { n - 1 } - 4 a _ { n - 2 } , \quad a _ { 0 } = 0 , a _ { 1 } = 1$

A vending machine dispensing books of stamps accepts only $1 coins, $1 bills, and $2 bills. Let an denote

describe each sequence recursively. Include initial conditions and assume that the sequences begin with a₁. -a_n = the number of ways to go down an n-step staircase if you go down 1, 2, or 3 steps at a time

describe each sequence recursively. Include initial conditions and assume that the sequences begin with a₁. -a_n = the number of bit strings of length n that contain a pair of consecutive 0's

determine whether the recurrence relation is a linear homogeneous recurrence relation with constant coeﬃcients. - $a _ { n } = n a _ { n - 1 }$

solve the recurrence relation either by using the characteristic equation or by discovering a pattern formed by the terms. - $a _ { n } = 2 a _ { n - 1 } + 5 , \quad a _ { 0 } = 3$

describe each sequence recursively. Include initial conditions and assume that the sequences begin with a₁. -a_n = the number of bit strings of length n with an even number of 0's

solve the recurrence relation either by using the characteristic equation or by discovering a pattern formed by the terms. - $a _ { n } = 2 a _ { n - 1 } + 2 a _ { n - 2 } , \quad a _ { 0 } = 0 , a _ { 1 } = 1$

solve the recurrence relation either by using the characteristic equation or by discovering a pattern formed by the terms. - $a _ { n } = 3 n a _ { n - 1 } , \quad a _ { 0 } = 2$

solve the recurrence relation either by using the characteristic equation or by discovering a pattern formed by the terms. - $a _ { n } = a _ { n - 1 } + 3 n , \quad a _ { 0 } = 5$

solve the recurrence relation either by using the characteristic equation or by discovering a pattern formed by the terms. - $a _ { n } = - 10 a _ { n - 1 } - 21 a _ { n - 2 } , \quad a _ { 0 } = 2 , a _ { 1 } = 1$

Quiz 8: A: Advanced Counting Techniques

determine whether the recurrence relation is a linear homogeneous recurrence relation with constant coeﬃcients. - an=5an−12−3an−22a _ { n } = 5 a _ { n - 1 } ^ { 2 } - 3 a _ { n - 2 } ^ { 2 }an​=5an−12​−3an−22​

Find the solution of the recurrence relation an = 3an−1 with a0 = 2.

determine whether the recurrence relation is a linear homogeneous recurrence relation with constant coeﬃcients. - an−7an−2+an−5=0a _ { n } - 7 a _ { n - 2 } + a _ { n - 5 } = 0an​−7an−2​+an−5​=0

determine whether the recurrence relation is a linear homogeneous recurrence relation with constant coeﬃcients. - an=0.7an−1−0.3an−2a _ { n } = 0.7 a _ { n - 1 } - 0.3 a _ { n - 2 }an​=0.7an−1​−0.3an−2​

determine whether the recurrence relation is a linear homogeneous recurrence relation with constant coeﬃcients. - an=an−3a _ { n } = a _ { n - 3 }an​=an−3​

describe each sequence recursively. Include initial conditions and assume that the sequences begin with a1. -an = the number of bit strings of length n that begin with 1

determine whether the recurrence relation is a linear homogeneous recurrence relation with constant coeﬃcients. - an+an−1=1a _ { n } + a _ { n - 1 } = 1an​+an−1​=1

solve the recurrence relation either by using the characteristic equation or by discovering a pattern formed by the terms. - an=5an−1−4an−2,a0=1,a1=0a _ { n } = 5 a _ { n - 1 } - 4 a _ { n - 2 } , \quad a _ { 0 } = 1 , a _ { 1 } = 0an​=5an−1​−4an−2​,a0​=1,a1​=0

solve the recurrence relation either by using the characteristic equation or by discovering a pattern formed by the terms. - an=an−2,a0=2,a1=−1a _ { n } = a _ { n - 2 } , \quad a _ { 0 } = 2 , a _ { 1 } = - 1an​=an−2​,a0​=2,a1​=−1

solve the recurrence relation either by using the characteristic equation or by discovering a pattern formed by the terms. - an=5an−1−4an−2,a0=0,a1=1a _ { n } = 5 a _ { n - 1 } - 4 a _ { n - 2 } , \quad a _ { 0 } = 0 , a _ { 1 } = 1an​=5an−1​−4an−2​,a0​=0,a1​=1

A vending machine dispensing books of stamps accepts only $1 coins, $1 bills, and $2 bills. Let an denote

describe each sequence recursively. Include initial conditions and assume that the sequences begin with a1. -an = the number of ways to go down an n-step staircase if you go down 1, 2, or 3 steps at a time

describe each sequence recursively. Include initial conditions and assume that the sequences begin with a1. -an = the number of bit strings of length n that contain a pair of consecutive 0's

determine whether the recurrence relation is a linear homogeneous recurrence relation with constant coeﬃcients. - an=nan−1a _ { n } = n a _ { n - 1 }an​=nan−1​

solve the recurrence relation either by using the characteristic equation or by discovering a pattern formed by the terms. - an=2an−1+5,a0=3a _ { n } = 2 a _ { n - 1 } + 5 , \quad a _ { 0 } = 3an​=2an−1​+5,a0​=3

describe each sequence recursively. Include initial conditions and assume that the sequences begin with a1. -an = the number of bit strings of length n with an even number of 0's

solve the recurrence relation either by using the characteristic equation or by discovering a pattern formed by the terms. - an=2an−1+2an−2,a0=0,a1=1a _ { n } = 2 a _ { n - 1 } + 2 a _ { n - 2 } , \quad a _ { 0 } = 0 , a _ { 1 } = 1an​=2an−1​+2an−2​,a0​=0,a1​=1

solve the recurrence relation either by using the characteristic equation or by discovering a pattern formed by the terms. - an=3nan−1,a0=2a _ { n } = 3 n a _ { n - 1 } , \quad a _ { 0 } = 2an​=3nan−1​,a0​=2

solve the recurrence relation either by using the characteristic equation or by discovering a pattern formed by the terms. - an=an−1+3n,a0=5a _ { n } = a _ { n - 1 } + 3 n , \quad a _ { 0 } = 5an​=an−1​+3n,a0​=5

solve the recurrence relation either by using the characteristic equation or by discovering a pattern formed by the terms. - an=−10an−1−21an−2,a0=2,a1=1a _ { n } = - 10 a _ { n - 1 } - 21 a _ { n - 2 } , \quad a _ { 0 } = 2 , a _ { 1 } = 1an​=−10an−1​−21an−2​,a0​=2,a1​=1

determine whether the recurrence relation is a linear homogeneous recurrence relation with constant coeﬃcients. - $a _ { n } = 5 a _ { n - 1 } ^ { 2 } - 3 a _ { n - 2 } ^ { 2 }$

Find the solution of the recurrence relation a_n = 3a_n−1 with a₀ = 2.

determine whether the recurrence relation is a linear homogeneous recurrence relation with constant coeﬃcients. - $a _ { n } - 7 a _ { n - 2 } + a _ { n - 5 } = 0$

determine whether the recurrence relation is a linear homogeneous recurrence relation with constant coeﬃcients. - $a _ { n } = 0.7 a _ { n - 1 } - 0.3 a _ { n - 2 }$

determine whether the recurrence relation is a linear homogeneous recurrence relation with constant coeﬃcients. - $a _ { n } = a _ { n - 3 }$

describe each sequence recursively. Include initial conditions and assume that the sequences begin with a₁. -a_n = the number of bit strings of length n that begin with 1

determine whether the recurrence relation is a linear homogeneous recurrence relation with constant coeﬃcients. - $a _ { n } + a _ { n - 1 } = 1$

solve the recurrence relation either by using the characteristic equation or by discovering a pattern formed by the terms. - $a _ { n } = 5 a _ { n - 1 } - 4 a _ { n - 2 } , \quad a _ { 0 } = 1 , a _ { 1 } = 0$

solve the recurrence relation either by using the characteristic equation or by discovering a pattern formed by the terms. - $a _ { n } = a _ { n - 2 } , \quad a _ { 0 } = 2 , a _ { 1 } = - 1$

solve the recurrence relation either by using the characteristic equation or by discovering a pattern formed by the terms. - $a _ { n } = 5 a _ { n - 1 } - 4 a _ { n - 2 } , \quad a _ { 0 } = 0 , a _ { 1 } = 1$

describe each sequence recursively. Include initial conditions and assume that the sequences begin with a₁. -a_n = the number of ways to go down an n-step staircase if you go down 1, 2, or 3 steps at a time

describe each sequence recursively. Include initial conditions and assume that the sequences begin with a₁. -a_n = the number of bit strings of length n that contain a pair of consecutive 0's

determine whether the recurrence relation is a linear homogeneous recurrence relation with constant coeﬃcients. - $a _ { n } = n a _ { n - 1 }$

solve the recurrence relation either by using the characteristic equation or by discovering a pattern formed by the terms. - $a _ { n } = 2 a _ { n - 1 } + 5 , \quad a _ { 0 } = 3$

describe each sequence recursively. Include initial conditions and assume that the sequences begin with a₁. -a_n = the number of bit strings of length n with an even number of 0's

solve the recurrence relation either by using the characteristic equation or by discovering a pattern formed by the terms. - $a _ { n } = 2 a _ { n - 1 } + 2 a _ { n - 2 } , \quad a _ { 0 } = 0 , a _ { 1 } = 1$

solve the recurrence relation either by using the characteristic equation or by discovering a pattern formed by the terms. - $a _ { n } = 3 n a _ { n - 1 } , \quad a _ { 0 } = 2$

solve the recurrence relation either by using the characteristic equation or by discovering a pattern formed by the terms. - $a _ { n } = a _ { n - 1 } + 3 n , \quad a _ { 0 } = 5$

solve the recurrence relation either by using the characteristic equation or by discovering a pattern formed by the terms. - $a _ { n } = - 10 a _ { n - 1 } - 21 a _ { n - 2 } , \quad a _ { 0 } = 2 , a _ { 1 } = 1$