Deck 9: Section 1: Infinite Series

Question 1

Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit.

A) The sequence diverges to 0.
B) The sequence diverges.
C) The sequence converges to 0.
D) The sequence converges to 1.
E) The sequence converges to .

Answer 1

The sequence converges to 0.

Question 2

Consider the sequence whose nth term is given by where P is the principal, is the account balance in dollars after n months, and r is the interest rate compounded annually. Find the fourth term of the sequence if and . Round your answer to two decimal places.

A) $9,296.08
B) $9,599.41
C) $9,396.38
D) $9,196.59
E) $9,236.29

Answer 2

$9,196.59

Question 3

Write an expression for the nth term of the sequence .

A)
B)
C)
D)
E)

Answer 3

Question 4

Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit.

A) The sequence converges to -1.
B) The sequence converges to 0.
C) The sequence diverges.
D) The sequence converges to 1.
E) The sequence diverges to 1.

Question 5

If the rate of inflation is % per year and the average price of a car is currently $40,000, the average price after n years is . Compute the average price after 6 years. Round your answer to two decimal places.

A) $32,301.59
B) $49,170.21
C) $248,400.00
D) $45,937.01
E) $231,600.00

Question 6

Write the first five terms of the sequence.

A)
B)
C)
D)
E)

Question 7

A deposit of $225 is made at the beginning of each month into an account at an annual interest rate of 3% compounded monthly. The balance in the account after n months is . Find the balance in the account after 4 years by computing the 48th term of the sequence. Round your answer to two decimal places.

A) $11,488.17
B) $905.64
C) $9,172.05
D) $24,404.88
E) $1,818.08

Question 8

Match the sequence with its graph.

A)
B)
C)
D)
E)

Question 9

Write the first three terms of the sequence.

A)
B)
C)
D)
E)

Question 10

Write the first five terms of the sequence.

A)
B)
C)
D)
E)

Question 11

Graph the sequence .

A)
B)
C)
D)
E)

Question 12

Match the sequence with its graph.

A)
B)
C)
D)
E)

Question 13

A government program that currently costs taxpayers $2.5 billion per year is cut back by 30 percent per year. Write an expression for the amount budgeted for this program after n years.

A)
B)
C)
D)
E)

Question 14

Write an expression for the nth term of the sequence .

A)
B)
C)
D)
E)

Question 15

Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit.

A) The sequence diverges.
B) The sequence converges to 2.
C) The sequence converges to -1.
D) The sequence converges to 1.
E) The sequence converges to 0.

Question 16

A government program that currently costs taxpayers $3.5 billion per year is cut back by 30 percent per year. Compute the budget after the fifth year. Round your answer to the nearest integer.

A) $1,552,968,594
B) $272,160,000
C) $8,505,000
D) $1,146,880,000
E) $588,245,000

Question 17

Write the next two apparent terms of the sequence .

A)
B)
C)
D)
E)