Question 1

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

Accepted Answer

C

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.

Accepted Answer

D

Question 3

Write an expression for the nth term of the sequence  .

Accepted Answer

B

Question 4

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

Accepted Answer

The answer of Determine the convergence or divergence of the...

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.

Accepted Answer

The answer of If the rate of inflation is ...

Question 6

Write the first five terms of the sequence.

Accepted Answer

The answer of Write the first five terms of the...

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.

Accepted Answer

The answer of A deposit of $225 is made at...

Question 8

Match the sequence with its graph.

Accepted Answer

The answer of Match the sequence with its graph. 
...

Question 9

Write the first three terms of the sequence.

Accepted Answer

The answer of Write the first three terms of the...

Question 10

Write the first five terms of the sequence.

Accepted Answer

The answer of Write the first five terms of the...

Question 11

Graph the sequence  .

Accepted Answer

The answer of Graph the sequence  .
...

Question 12

Match the sequence with its graph.

Accepted Answer

The graph in option B starts at the origin, increases at a constant rate, then decreases at a constant rate and ends at 0. This matches the given sequence.

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.

Accepted Answer

The expression for the amount budgeted after n years can be written as:
2.5 billion * (0.7)^n
where n is the number of years. 
Substituting n with 1, we get:
2.5 billion * (0.7)^1 = 1.75 billion
So, after the first year, the program will be budgeted at 1.75 billion. 
Substituting n with 2, we get:
2.5 billion * (0.7)^2 = 1.225 billion
So, after the second year, the program will be budgeted at 1.225 billion. 
The same pattern follows for subsequent years. 
Therefore, 11eaa595_6493_81dd_a696_cb5e0c647b21_TB4584_11_TB4584_11 is the correct answer.

Question 14

Write an expression for the nth term of the sequence  .

Accepted Answer

The sequence has the pattern of adding 1 to the 9th digit (from the left) in each term, which is initially '4'. Therefore, the nth term will have the digit '4' replaced by 'n-1'. The only option that fits this pattern is D, where the 9th digit is '8' in the second term, corresponding to n=2.

Question 15

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

Accepted Answer

The answer of Determine the convergence or divergence of the...

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.

Accepted Answer

The budget decreases by 30% each year, so it retains 70% of its value annually. After 5 years, the budget is $3.5 billion * (0.7)^5, which equals approximately $588,245,000.

Question 17

Write the next two apparent terms of the sequence  .

Accepted Answer

By looking at the pattern, it seems like the fourth group of characters is increasing by one for each term. Therefore, the next term should have 37d2 instead of 10c0. The rest of the sequence remains the same.

Quiz 9: Section 1: Infinite Series

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

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.

Write an expression for the nth term of the sequence .

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

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.

Write the first five terms of the sequence.

Match the sequence with its graph.

Write the first three terms of the sequence.

Write the first five terms of the sequence.

Graph the sequence .

Match the sequence with its graph.

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.

Write an expression for the nth term of the sequence .

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

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.

Write the next two apparent terms of the sequence .