Question 1

Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given.
-a = 2; 
A) 
B) 
C) 
D)a

Accepted Answer

The answer of Find the fifth term and the nth...

Question 2

Find the indicated term of the geometric sequence.
-6th term of -1, 3, -9, ...
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the indicated term of the geometric...

Question 3

Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the
common difference; if it is geometric, find the common ratio.
-3 - 1n
A)Arithmetic; d = - 1
B)Geometric; r = - 1
C)Arithmetic; d =3
D)Neither

Accepted Answer

The sequence 3 - 1n is arithmetic with a common difference (d) of -1, as each term decreases by 1 from the previous term.

Question 4

Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given.
-a = 7; r = -3
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the fifth term and the nth...

Question 5

Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the
common difference; if it is geometric, find the common ratio.
-
A)Arithmetic; d = -4
B)Geometric; r = 3
C)Arithmetic; d = 3
D)Neither

Accepted Answer

The answer of Determine whether the given sequence is arithmetic,...

Question 6

Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given.
-a = 3; r = 2
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the fifth term and the nth...

Question 7

Find the indicated term of the geometric sequence.
-8th term of 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the indicated term of the geometric...

Question 8

Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the
common difference; if it is geometric, find the common ratio.
-1, -3, 9, -27, 81, ...
A)Geometric; r = -3
B)Geometric; r = 3
C)Arithmetic; d = -4
D)Neither

Accepted Answer

The given sequence is geometric because each term is obtained by multiplying the previous term by -3. Therefore, the common ratio is -3. The given sequence is formed by repeatedly multiplying by -3, making it a geometric sequence. Therefore, the common ratio is -3.

Question 9

Find the indicated term of the geometric sequence.
-7th term of 0.2, 0.02, 0.002, . . .
A)0.0000002
B)0.00000002
C)0.000002
D)0

Accepted Answer

The common ratio (r) of the sequence is 0.02 / 0.2 = 0.1. The nth term of a geometric sequence is given by $a_n = a_1 \cdot r^{(n-1)}$, where $a_1$ is the first term, $r$ is the common ratio, and $n$ is the term number. For the 7th term: $a_7 = 0.2 \cdot (0.1)^{7-1} = 0.2 \cdot (0.1)^6 = 0.2 \cdot 0.000001 = 0.0000002$.

Question 10

Find the nth term {an} of the geometric sequence. When given, r is the common ratio.
-a = -2; r = -6
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the nth term {an} of the...

Question 11

Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the
common difference; if it is geometric, find the common ratio.
-
A)Geometric; 
B)Arithmetic; 
C)Geometric; 
D)Neither

Accepted Answer

The answer of Determine whether the given sequence is arithmetic,...

Question 12

Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the
common difference; if it is geometric, find the common ratio.
-
A)Geometric; 
B)Arithmetic; d = 5
C)Geometric; r = 5
D)Neither

Accepted Answer

The answer of Determine whether the given sequence is arithmetic,...

Question 13

Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given.
-
A) 
B)a 
C) 
D)

Accepted Answer

The answer of Find the fifth term and the nth...

Question 14

Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the
common difference; if it is geometric, find the common ratio.
-9, 11, 14,18, ...
A)Geometric; r = 9
B)Arithmetic; d = 9
C)Geometric; r = 81
D)Neither

Accepted Answer

The sequence is neither arithmetic nor geometric because the differences between consecutive terms (2, 3, 4) are not constant, and the ratios between consecutive terms are also not constant.

Question 15

Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the
common difference; if it is geometric, find the common ratio.
-
A)Geometric; 
B)Arithmetic; d 
C)Geometric; r = 6
D)Neither

Accepted Answer

The sequence given is: 11, 22, 44, 88, 176...
The terms are being multiplied by 2 to get the next term, which means it is a geometric sequence with a common ratio of 2. The sequence is geometric because each term is being multiplied by a constant factor. The common ratio is not provided in this question.

Question 16

Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given.
-
A) 
B) 
C) 
D)

Accepted Answer

The fifth term of a geometric sequence with initial term $a$ and common ratio $r$ is $ar^4$ (since we are finding the 5th term, which is 4 terms after the first term). 
The nth term of a geometric sequence with initial term $a$ and common ratio $r$ is $ar^{n-1}$.

Therefore, the fifth term is $a r^4$, and the nth term is $ar^{n-1}$.

Using the values given in the question: 
a = 11ebbed0_ca32_4836_8acb_3fe1f68b6fd7_TB8253_11 
r = TB8253_11

The fifth term is $(11ebbed0\_ca32\_4836\_8acb\_3fe1f68b6fd7\_TB8253\_11)(TB8253_{11})^4 = 11ebbed0\_ca32\_4837\_8acb\_996a56944647\_TB8253\_11$

The nth term is $(11ebbed0\_ca32\_4836\_8acb\_3fe1f68b6fd7\_TB8253\_11)(TB8253_{11})^{n-1}$

Question 17

Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given.
-a = -7; r = -3
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the fifth term and the nth...

Question 18

Find the nth term {an} of the geometric sequence. When given, r is the common ratio.
-a = -3; 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the nth term {an} of the...

Question 19

Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the
common difference; if it is geometric, find the common ratio.
-3, 5, 7, 11, 13, ...
A)Geometric; r = 2
B)Arithmetic; d = 2
C)Arithmetic; d = 4
D)Neither

Accepted Answer

The sequence consists of prime numbers, which do not increase by a constant difference (arithmetic) nor multiply by a constant factor (geometric).

Question 20

Find the indicated term of the geometric sequence.
-6th term of 1, 3, 9, ...
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the indicated term of the geometric...

Quiz 9: Sequences; Induction; the Binomial Theorem

Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given. -a = 2;

Find the indicated term of the geometric sequence. -6th term of -1, 3, -9, ...

Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. -3 - 1n

Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given. -a = 7; r = -3

Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. -

Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given. -a = 3; r = 2

Find the indicated term of the geometric sequence. -8th term of

Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. -1, -3, 9, -27, 81, ...

Find the indicated term of the geometric sequence. -7th term of 0.2, 0.02, 0.002, . . .

Find the nth term {an} of the geometric sequence. When given, r is the common ratio. -a = -2; r = -6

Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. -

Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. -

Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given. -

Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. -9, 11, 14,18, ...

Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. -

Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given. -

Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given. -a = -7; r = -3

Find the nth term {an} of the geometric sequence. When given, r is the common ratio. -a = -3;

Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. -3, 5, 7, 11, 13, ...

Find the indicated term of the geometric sequence. -6th term of 1, 3, 9, ...