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Chapter 12: Q. 11 (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.

3,32,34,38,316,..

Short Answer

Expert verified
  • Given sequence is a geometric sequence.
  • Its common ratio is r=12.
  • Sum of first nterm is Sn=61-2-n.

Step by step solution

01

Step 1. Given information. 

Sequence is:3,32,34,38,316,.......

02

Step 2. To find common ratio.

The ratio between two successive term is :

r=323=12

r=3432=12

Since all the ratio of successive term in the sequence is constant.

Hence it is a geometric sequence, whose common ratio isr=12

03

Step 3. To find sum of first nterms.

First term is a=3

common ratio isr=12

So sum of n terms is:

Sn=a(1-rn)1-r=3.1-12n1-12=3(1-2-n)12=6(1-2-n)

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