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Chapter 12: Q 33. (page 825)

In Problems 31鈥�38, find the nth term anof each geometric sequence. When given, r is the common ratio.

-3,-1,-13,19,...

Short Answer

Expert verified

The common ratio isr=-13and the nth term is-3路-13n-1

Step by step solution

01

Step 1. Write the given information.

The given geometric sequence is-3,1,-13,-19,...

02

Step 2. Find the common ratio.

a1=-3,a2=1,a3=-13a2a1=-13a3a2=-131=-13r=-13

03

Step 3. Find the nth term.

The formula for the nth term is an=a1路rn-1

an=-3路-13n-1

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Most popular questions from this chapter

Roth IRA On January 1, 1999, Bob decided to place \(500 at the end of each quarter into a Roth Individual Retirement Account.

(a) Find a recursive formula that represents Bob鈥檚 balance at the end of each quarter if the rate of return is assumed to be 8% per annum compounded quarterly.

(b) How long will it be before the value of the account exceeds \)100,000?

(c) What will be the value of the account in 25 years when Bob retires?

In Problems 37鈥�50, a sequence is defined recursively. Write down the first five terms.

a1=1;a2=2;an=an-1路an-2

In Problems 51鈥�66, determine whether each infinite geometric series converges or diverges. If it converges, find its sum.

8+12+18+27+....

A(n) _______ is a function whose domain is the set of positive integers.

In Problems 17鈥�28, write down the first five terms of each sequence.

dn=(-1)n-1n2n-1
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