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Chapter 12: Q. 9 (page 838)

In Problems 7鈥�12, determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference and the sum of the first n terms. If the sequence is geometric, find the common ratio and the sum of the first n terms.

sn=23n

Short Answer

Expert verified
  • Given sequence is a geometric sequence.
  • The common ratio of the sequence is 8.
  • Th sum of first nterms is:Sn=878n-1

Step by step solution

01

Step 1. Given information

Sequence:sn=23n

02

Step 2. To find first term and n-1th term.

s1=23.1=23=8

sn-1=23(n-1)=23n-3=23n23

03

Step 3. To find ratio between two successive terms.

Ratio between two successive terms is:

r=snsn-1=23n23n23=23=8

Since ratio is constant.

Hence the given sequence is a geometric sequence whose common ratio is 8.

04

Step 4. To find sum of first n term of the sequence.

Sn=88n-18-1Sn=878n-1

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Most popular questions from this chapter

In Problems 51鈥�60, write out each sum.

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In Problems 29鈥�36, the given pattern continues. Write down the nth term of a sequence ansuggested by the pattern.

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

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

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

In Problems 11鈥�16, evaluate each factorial expression.

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