Exam 54: Geometric Sequences and Series

Write an expression for the nth term of the geometric sequence.Then find the indicated term.(Round your answer to three decimal places. )? $a _ { 1 } = 2500 , r = 1.005 , n = 60$ ?

Free

(Multiple Choice)

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Question 1

Correct Answer:

Verified

B

Match the geometric sequence with its graph from the choices below.? $a _ { n } = - 3 \left( \frac { 2 } { 5 } \right) ^ { n - 1 }$

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(Multiple Choice)

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Question 2

Correct Answer:

Verified

B

?Find the indicated nth term of the geometric sequence. ? 7th term: $a _ { 4 } = - \frac { 4 } { 27 } , a _ { 10 } = - \frac { 4 } { 19,683 }$ ?

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(Multiple Choice)

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Question 3

Correct Answer:

Verified

D

A principal of $2000 is invested at 5% interest.Find the amount after 10 years if the interest is compounded annually.

(Multiple Choice)

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Question 4

Find the sum using the formulas for the sums of powers of integers. $\sum _ { n = 1 } ^ { 8 } n ^ { 3 }$

(Multiple Choice)

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Question 5

Use mathematical induction to prove the formula for every positive integer n.Show all your work. $\sum _ { i = 1 } ^ { n } i ( i + 4 ) = \frac { n ( n + 1 ) ( 2 n + 13 ) } { 6 }$

(Essay)

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Question 6

Determine whether the sequence is geometric.If so,find the common ratio. -3,-6,-12,-24,...

(Multiple Choice)

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Question 7

Find the sum of the finite geometric sequence.(Round your answer to three decimal places. )? $\sum _ { n = 0 } ^ { 6 } 900 ( 1.04 ) ^ { n }$ ?

(Multiple Choice)

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Question 8

Determine whether the sequence is geometric.If so,find the common ratio.? $4,20,100,500 , \ldots$ ?

(Multiple Choice)

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Question 9

Find the sum of the infinite geometric series.(Round your answer to the nearest whole number. )? $\sum _ { n = 0 } ^ { \infty } \left( \frac { 1 } { 8 } \right) ^ { n }$ ?

(Multiple Choice)

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Question 10

Determine whether the sequence is geometric.If so,find the common ratio.? $55,50,45,40 , \ldots$ ?

(Multiple Choice)

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Question 11

A principal of $3000 is invested at 5% interest.Find the amount after 20 years if the interest is compounded monthly.

(Multiple Choice)

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Question 12

Find the sum of the indicated terms of the geometric sequence. 6,18,54 ...(to 8 terms)

(Multiple Choice)

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Question 13

Determine whether the sequence is geometric.If so,find the common ratio.? $7,21,63,189 , \ldots$ ?

(Multiple Choice)

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Question 14

Find the sum of the infinite geometric series.? $\sum _ { n = 0 } ^ { \infty } 9 \left( \frac { 9 } { 10 } \right) ^ { n }$ ?

(Multiple Choice)

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Question 15

Find the sum of the indicated terms of the geometric sequence. $\sum _ { n = 1 } ^ { n = 5 } 6 ( 2 ) ^ { n - 1 }$

(Short Answer)

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Question 16

Find the indicated nth term of the geometric sequence. ? 10th term : $7,28,112 , \ldots$ ?

(Multiple Choice)

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Question 17

Use mathematical induction to prove the formula for every positive integer n.Show all your work. $+ 6 + 11 + 16 + 21 + \ldots + ( 5 n + 1 ) = \frac { n } { 2 } ( 5 n + 7 )$

(Essay)

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Question 18

Use summation notation to write the sum. $- 3 - 6 - 12 - \ldots - 48$

(Multiple Choice)

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Question 19

Find the sum of the infinite geometric series.? $\sum _ { n = 0 } ^ { \infty } 4 ( 0.8 ) ^ { n }$ ?

(Multiple Choice)

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Question 20

Exam 54: Geometric Sequences and Series

Write an expression for the nth term of the geometric sequence.Then find the indicated term.(Round your answer to three decimal places. )? a1=2500,r=1.005,n=60a _ { 1 } = 2500 , r = 1.005 , n = 60a1​=2500,r=1.005,n=60 ?

Match the geometric sequence with its graph from the choices below.? an=−3(25)n−1a _ { n } = - 3 \left( \frac { 2 } { 5 } \right) ^ { n - 1 }an​=−3(52​)n−1

?Find the indicated nth term of the geometric sequence. ? 7th term: a4=−427,a10=−419,683a _ { 4 } = - \frac { 4 } { 27 } , a _ { 10 } = - \frac { 4 } { 19,683 }a4​=−274​,a10​=−19,6834​ ?

A principal of $2000 is invested at 5% interest.Find the amount after 10 years if the interest is compounded annually. ​

Find the sum using the formulas for the sums of powers of integers. ∑n=18n3\sum _ { n = 1 } ^ { 8 } n ^ { 3 }∑n=18​n3

Use mathematical induction to prove the formula for every positive integer n.Show all your work. ∑i=1ni(i+4)=n(n+1)(2n+13)6\sum _ { i = 1 } ^ { n } i ( i + 4 ) = \frac { n ( n + 1 ) ( 2 n + 13 ) } { 6 }∑i=1n​i(i+4)=6n(n+1)(2n+13)​

Determine whether the sequence is geometric.If so,find the common ratio. -3,-6,-12,-24,...

Find the sum of the finite geometric sequence.(Round your answer to three decimal places. )? ∑n=06900(1.04)n\sum _ { n = 0 } ^ { 6 } 900 ( 1.04 ) ^ { n }∑n=06​900(1.04)n ?

Determine whether the sequence is geometric.If so,find the common ratio.? 4,20,100,500,…4,20,100,500 , \ldots4,20,100,500,… ?

Find the sum of the infinite geometric series.(Round your answer to the nearest whole number. )? ∑n=0∞(18)n\sum _ { n = 0 } ^ { \infty } \left( \frac { 1 } { 8 } \right) ^ { n }∑n=0∞​(81​)n ?

Determine whether the sequence is geometric.If so,find the common ratio.? 55,50,45,40,…55,50,45,40 , \ldots55,50,45,40,… ?

A principal of $3000 is invested at 5% interest.Find the amount after 20 years if the interest is compounded monthly. ​

Find the sum of the indicated terms of the geometric sequence. ​ 6,18,54 ...(to 8 terms) ​

Determine whether the sequence is geometric.If so,find the common ratio.? 7,21,63,189,…7,21,63,189 , \ldots7,21,63,189,… ?

Find the sum of the infinite geometric series.? ∑n=0∞9(910)n\sum _ { n = 0 } ^ { \infty } 9 \left( \frac { 9 } { 10 } \right) ^ { n }∑n=0∞​9(109​)n ?

Find the sum of the indicated terms of the geometric sequence.​ ∑n=1n=56(2)n−1\sum _ { n = 1 } ^ { n = 5 } 6 ( 2 ) ^ { n - 1 }∑n=1n=5​6(2)n−1

Find the indicated nth term of the geometric sequence. ? 10th term : 7,28,112,…7,28,112 , \ldots7,28,112,… ?

Use mathematical induction to prove the formula for every positive integer n.Show all your work. +6+11+16+21+…+(5n+1)=n2(5n+7)+ 6 + 11 + 16 + 21 + \ldots + ( 5 n + 1 ) = \frac { n } { 2 } ( 5 n + 7 )+6+11+16+21+…+(5n+1)=2n​(5n+7)

Use summation notation to write the sum. −3−6−12−…−48- 3 - 6 - 12 - \ldots - 48−3−6−12−…−48

Find the sum of the infinite geometric series.? ∑n=0∞4(0.8)n\sum _ { n = 0 } ^ { \infty } 4 ( 0.8 ) ^ { n }∑n=0∞​4(0.8)n ?

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Write an expression for the nth term of the geometric sequence.Then find the indicated term.(Round your answer to three decimal places. )? $a _ { 1 } = 2500 , r = 1.005 , n = 60$ ?

Match the geometric sequence with its graph from the choices below.? $a _ { n } = - 3 \left( \frac { 2 } { 5 } \right) ^ { n - 1 }$

?Find the indicated nth term of the geometric sequence. ? 7th term: $a _ { 4 } = - \frac { 4 } { 27 } , a _ { 10 } = - \frac { 4 } { 19,683 }$ ?

A principal of $2000 is invested at 5% interest.Find the amount after 10 years if the interest is compounded annually.

Find the sum using the formulas for the sums of powers of integers. $\sum _ { n = 1 } ^ { 8 } n ^ { 3 }$

Use mathematical induction to prove the formula for every positive integer n.Show all your work. $\sum _ { i = 1 } ^ { n } i ( i + 4 ) = \frac { n ( n + 1 ) ( 2 n + 13 ) } { 6 }$

Find the sum of the finite geometric sequence.(Round your answer to three decimal places. )? $\sum _ { n = 0 } ^ { 6 } 900 ( 1.04 ) ^ { n }$ ?

Determine whether the sequence is geometric.If so,find the common ratio.? $4,20,100,500 , \ldots$ ?

Find the sum of the infinite geometric series.(Round your answer to the nearest whole number. )? $\sum _ { n = 0 } ^ { \infty } \left( \frac { 1 } { 8 } \right) ^ { n }$ ?

Determine whether the sequence is geometric.If so,find the common ratio.? $55,50,45,40 , \ldots$ ?

A principal of $3000 is invested at 5% interest.Find the amount after 20 years if the interest is compounded monthly.

Find the sum of the indicated terms of the geometric sequence. 6,18,54 ...(to 8 terms)

Determine whether the sequence is geometric.If so,find the common ratio.? $7,21,63,189 , \ldots$ ?

Find the sum of the infinite geometric series.? $\sum _ { n = 0 } ^ { \infty } 9 \left( \frac { 9 } { 10 } \right) ^ { n }$ ?

Find the sum of the indicated terms of the geometric sequence. $\sum _ { n = 1 } ^ { n = 5 } 6 ( 2 ) ^ { n - 1 }$

Find the indicated nth term of the geometric sequence. ? 10th term : $7,28,112 , \ldots$ ?

Use mathematical induction to prove the formula for every positive integer n.Show all your work. $+ 6 + 11 + 16 + 21 + \ldots + ( 5 n + 1 ) = \frac { n } { 2 } ( 5 n + 7 )$

Use summation notation to write the sum. $- 3 - 6 - 12 - \ldots - 48$

Find the sum of the infinite geometric series.? $\sum _ { n = 0 } ^ { \infty } 4 ( 0.8 ) ^ { n }$ ?