Question 1

Write a formula for the general term (the nth term) of the geometric sequence.
-$$\frac { 1 } { 8 } , - \frac { 1 } { 40 } , \frac { 1 } { 200 } , - \frac { 1 } { 1000 } , \ldots$$
A) $a _ { n } = \frac { 1 } { 8 } - \frac { 1 } { 5 } ( n - 1 )$
B) $a _ { n } = \frac { 1 } { 5 } \left( - \frac { 1 } { 8 } \right) ^ { n - 1 }$
C) $a _ { n } = \frac { 1 } { 8 } \left( - \frac { 1 } { 5 } \right) ^ { n - 1 }$
D) $a _ { n } = \left( \frac { 1 } { 8 } \right) ^ { n - 1 } - \frac { 3 } { 20 }$

Accepted Answer

The sequence is geometric with the first term $a_1 = \frac{1}{8}$ and common ratio $r = -\frac{1}{5}$, so the nth term is given by $a_n = a_1 \cdot r^{n-1}$.

Question 2

Write a formula for the general term (the nth term) of the geometric sequence.
-$- 8 , - 16 , - 32 , - 64 , - 128 , \ldots$
A) $a _ { n } = - 8 ( 2 n )$
B) $a _ { n } = - 8 ( 2 ) ^ { n }$
C) $a _ { n } = - 8 ( 2 ) ^ { n - 1 }$
D) $a _ { n } = a _ { 1 } + 2 ^ { n }$

Accepted Answer

The sequence is a geometric sequence with the first term $a_1 = -8$ and common ratio $r = 2$. The formula for the nth term of a geometric sequence is $a_n = a_1 \cdot r^{n-1}$. Substituting $a_1 = -8$ and $r = 2$ gives $a_n = -8 \cdot 2^{n-1}$.

Question 3

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r.
-$$\text { Find } a _ { 4 } \text { when } a _ { 1 } = 8 , r = - 5 \text {. }$$
A) -1000
B) 5000
C) 1000
D) -125

Accepted Answer

The formula for the nth term of a geometric sequence is $a_n = a_1 \cdot r^{(n-1)}$. For $a_4$, $n = 4$, $a_1 = 8$, and $r = -5$, so $a_4 = 8 \cdot (-5)^{4-1} = 8 \cdot (-5)^3 = 8 \cdot (-125) = -1000$.

Question 4

Write a formula for the general term (the nth term) of the geometric sequence.
-$6,12,24,48,96 , \ldots$
A) $a _ { n } = 6 ( 2 ) ^ { n - 1 }$
B) $a _ { n } = a _ { 1 } + 2 ^ { n }$
C) $a _ { n } = 6 ( 2 n )$
D) $a _ { n } = 6 ( 2 ) ^ { \mathrm { n } }$

Accepted Answer

The sequence is geometric with the first term $a_1 = 6$ and common ratio $r = 2$. The formula for the nth term of a geometric sequence is $a_n = a_1 \cdot r^{n-1}$, which matches choice A.

Question 5

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r.
-Find a8 when a1 = 20,000, r = -0.1.
A) -0.002
B) 0.002
C) 0.0002
D) -0.02

Accepted Answer

The formula for the nth term of a geometric sequence is given by $ a_n = a_1 \cdot r^{(n-1)} $. For this problem, $ a_1 = 20,000 $, $ r = -0.1 $, and $ n = 8 $. Plugging these values into the formula gives $ a_8 = 20,000 \cdot (-0.1)^{7} = 20,000 \cdot (-0.0000001) = -0.002 $.

Question 6

Write a formula for the general term (the nth term) of the geometric sequence.
-$3,1 , \frac { 1 } { 3 } , \frac { 1 } { 9 } , \frac { 1 } { 27 } , \ldots$
A) $a _ { n } = 3 \left( \frac { 1 } { 9 } \right) ^ { n - 1 }$
B) $a _ { n } = 3 \left( \frac { 1 } { 3 } \right) ^ { n }$
C) $\mathrm { a } _ { \mathrm { n } } = 3 \left( \frac { 1 } { 3 } \right) ^ { \mathrm { n } - 1 }$
D) $a _ { n } = 3 \left( \frac { 1 } { 3 } \right) ^ { n + 1 }$

Accepted Answer

The sequence is geometric with the first term $a_1 = 3$ and common ratio $r = \frac{1}{3}$. The formula for the nth term of a geometric sequence is $a_n = a_1 \cdot r^{n-1}$, which matches choice C.

Question 7

Write a formula for the general term (the nth term) of the geometric sequence.
-$$3 , - 1 , \frac { 1 } { 3 } , - \frac { 1 } { 9 } , \frac { 1 } { 27 } , \ldots$$
A) $a _ { n } = 3 \left( - \frac { 1 } { 3 } \right) ^ { n }$
B) $a _ { n } = 3 \left( - \frac { 1 } { 3 } \right) ^ { n + 1 }$
C) $a _ { n } = 3 \left( - \frac { 1 } { 9 } \right) ^ { n - 1 }$
D) $a _ { n } = 3 \left( - \frac { 1 } { 3 } \right) ^ { n - 1 }$

Accepted Answer

The sequence is geometric with the first term $a_1 = 3$ and a common ratio $r = -\frac{1}{3}$. The formula for the nth term of a geometric sequence is $a_n = a_1 \cdot r^{n-1}$, which matches option D.

Question 8

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r.
-$$\text { Find } a _ { 10 } \text { when } a _ { 1 } = 2 , r = 2$$
A) 1024
B) 1028
C) 20
D) 2048

Accepted Answer

The formula for the nth term of a geometric sequence is $a_n = a_1 \cdot r^{(n-1)}$. Substituting $a_1 = 2$, $r = 2$, and $n = 10$, we get $a_{10} = 2 \cdot 2^{(10-1)} = 2 \cdot 2^9 = 2 \cdot 512 = 1024$.

Question 9

Write a formula for the general term (the nth term) of the geometric sequence.
-$2 , - 4,8 , - 16,32 , \ldots$
A) $a _ { n } = 2 ( - 2 ) ^ { n - 1 }$
B) $a _ { n } = a _ { 1 } - 2 ^ { n }$
C) $a _ { n } = 2 ( - 2 n )$
D) $a _ { n } = 2 ( - 2 ) ^ { n }$

Accepted Answer

The sequence is geometric with the first term $a_1 = 2$ and common ratio $r = -2$. The formula for the nth term of a geometric sequence is $a_n = a_1 \cdot r^{n-1}$, which simplifies to $a_n = 2 \cdot (-2)^{n-1}$ for this sequence.

Question 10

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r.
-Find $a _ { 6 }$ when $a _ { 1 } = 3200 , r = - \frac { 1 } { 2 }$.
A) 100
B) $- 100$
C) $- 50$
D) $- 10$

Accepted Answer

The formula for the nth term of a geometric sequence is $a_n = a_1 \cdot r^{n-1}$. Plugging in the given values, $a_6 = 3200 \cdot (-\frac{1}{2})^{6-1} = 3200 \cdot (-\frac{1}{2})^5 = 3200 \cdot -\frac{1}{32} = -100$.

Question 11

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r.
-Find a 10 when a $1 = 1000 , r = \frac { 1 } { 3 }$.
A) $\frac { 1000 } { 59,049 }$
B) $\frac { 1000 } { 19,683 }$
C) $\frac { 1000 } { 177,147 }$
D) 1003

Accepted Answer

The nth term of a geometric sequence is given by $ a_n = a_1 \cdot r^{(n-1)} $. For the 10th term, $ a_{10} = 1000 \cdot \left(\frac{1}{3}\right)^9 = \frac{1000}{19,683} $.

Question 12

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. -Find a₉ when a₁ = -4, r = 2. A) 12 B) -2048 C) -1024 D) -1020

Accepted Answer

The nth term of a geometric sequence is given by a_n = a_1 * r^(n-1). For a_9, substitute a_1 = -4, r = 2, and n = 9: a_9 = -4 * 2^(9-1) = -4 * 256 = -1024.

Question 13

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. -Find a₉ when a₁ = 2, r = -2. A) 516 B) -1024 C) -14 D) 512

Accepted Answer

The answer of Use the formula for the general term...

Question 14

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r.
-Find a8 when a1 = 2,000,000, r = 0.1.
A) 0.002
B) 2
C) 0.02
D) 0.2

Accepted Answer

The answer of Use the formula for the general term...

Question 15

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. -Find a₈ when a1 = -3, r = -2. A) 388 B) 384 C) -17 D) -768

Accepted Answer

The answer of Use the formula for the general term...

Quiz 8: Quadratic Equations and Functions

Write a formula for the general term (the nth term) of the geometric sequence. - $\frac { 1 } { 8 } , - \frac { 1 } { 40 } , \frac { 1 } { 200 } , - \frac { 1 } { 1000 } , \ldots$

Write a formula for the general term (the nth term) of the geometric sequence. - $- 8 , - 16 , - 32 , - 64 , - 128 , \ldots$

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. - $\text { Find } a _ { 4 } \text { when } a _ { 1 } = 8 , r = - 5 \text {. }$

Write a formula for the general term (the nth term) of the geometric sequence. - $6,12,24,48,96 , \ldots$

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. -Find a8 when a1 = 20,000, r = -0.1.

Write a formula for the general term (the nth term) of the geometric sequence. - $3,1 , \frac { 1 } { 3 } , \frac { 1 } { 9 } , \frac { 1 } { 27 } , \ldots$

Write a formula for the general term (the nth term) of the geometric sequence. - $3 , - 1 , \frac { 1 } { 3 } , - \frac { 1 } { 9 } , \frac { 1 } { 27 } , \ldots$

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. - $\text { Find } a _ { 10 } \text { when } a _ { 1 } = 2 , r = 2$

Write a formula for the general term (the nth term) of the geometric sequence. - $2 , - 4,8 , - 16,32 , \ldots$

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. -Find $a _ { 6 }$ when $a _ { 1 } = 3200 , r = - \frac { 1 } { 2 }$ .

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. -Find a 10 when a $1 = 1000 , r = \frac { 1 } { 3 }$ .

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. -Find a₉ when a₁ = -4, r = 2.

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. -Find a₉ when a₁ = 2, r = -2.

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. -Find a8 when a1 = 2,000,000, r = 0.1.

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. -Find a₈ when a1 = -3, r = -2.

Quiz 8: Quadratic Equations and Functions

Write a formula for the general term (the nth term) of the geometric sequence. - 18,−140,1200,−11000,…\frac { 1 } { 8 } , - \frac { 1 } { 40 } , \frac { 1 } { 200 } , - \frac { 1 } { 1000 } , \ldots81​,−401​,2001​,−10001​,…

Write a formula for the general term (the nth term) of the geometric sequence. - −8,−16,−32,−64,−128,…- 8 , - 16 , - 32 , - 64 , - 128 , \ldots−8,−16,−32,−64,−128,…

Write a formula for the general term (the nth term) of the geometric sequence. - 6,12,24,48,96,…6,12,24,48,96 , \ldots6,12,24,48,96,…

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. -Find a8 when a1 = 20,000, r = -0.1.

Write a formula for the general term (the nth term) of the geometric sequence. - 3,1,13,19,127,…3,1 , \frac { 1 } { 3 } , \frac { 1 } { 9 } , \frac { 1 } { 27 } , \ldots3,1,31​,91​,271​,…

Write a formula for the general term (the nth term) of the geometric sequence. - 3,−1,13,−19,127,…3 , - 1 , \frac { 1 } { 3 } , - \frac { 1 } { 9 } , \frac { 1 } { 27 } , \ldots3,−1,31​,−91​,271​,…

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. - Find a10 when a1=2,r=2\text { Find } a _ { 10 } \text { when } a _ { 1 } = 2 , r = 2 Find a10​ when a1​=2,r=2

Write a formula for the general term (the nth term) of the geometric sequence. - 2,−4,8,−16,32,…2 , - 4,8 , - 16,32 , \ldots2,−4,8,−16,32,…

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. -Find a6a _ { 6 }a6​ when a1=3200,r=−12a _ { 1 } = 3200 , r = - \frac { 1 } { 2 }a1​=3200,r=−21​ .

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. -Find a 10 when a 1=1000,r=131 = 1000 , r = \frac { 1 } { 3 }1=1000,r=31​ .

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. -Find a9 when a1 = -4, r = 2.

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. -Find a9 when a1 = 2, r = -2.

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. -Find a8 when a1 = 2,000,000, r = 0.1.

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. -Find a8 when a1 = -3, r = -2.

Write a formula for the general term (the nth term) of the geometric sequence. - $\frac { 1 } { 8 } , - \frac { 1 } { 40 } , \frac { 1 } { 200 } , - \frac { 1 } { 1000 } , \ldots$

Write a formula for the general term (the nth term) of the geometric sequence. - $- 8 , - 16 , - 32 , - 64 , - 128 , \ldots$

Write a formula for the general term (the nth term) of the geometric sequence. - $6,12,24,48,96 , \ldots$

Write a formula for the general term (the nth term) of the geometric sequence. - $3,1 , \frac { 1 } { 3 } , \frac { 1 } { 9 } , \frac { 1 } { 27 } , \ldots$

Write a formula for the general term (the nth term) of the geometric sequence. - $3 , - 1 , \frac { 1 } { 3 } , - \frac { 1 } { 9 } , \frac { 1 } { 27 } , \ldots$

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. - $\text { Find } a _ { 10 } \text { when } a _ { 1 } = 2 , r = 2$

Write a formula for the general term (the nth term) of the geometric sequence. - $2 , - 4,8 , - 16,32 , \ldots$

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. -Find $a _ { 6 }$ when $a _ { 1 } = 3200 , r = - \frac { 1 } { 2 }$ .

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. -Find a 10 when a $1 = 1000 , r = \frac { 1 } { 3 }$ .

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. -Find a₉ when a₁ = -4, r = 2.

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. -Find a₉ when a₁ = 2, r = -2.

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. -Find a₈ when a1 = -3, r = -2.