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Chapter 12: Q 7. (page 824)

Show that each sequence is geometric. Then find the common ratio and write out the first four termssn=3n.

Short Answer

Expert verified

The common ratio is3and the first four terms are3,9,27,81.

Step by step solution

01

Step 1. Given information.

We have given sequence sn=3n.

The nth term and (n-1)th term aresn=3nsn-1=3n-1

02

Step 2. To find the common ratio.

We have,

r=snsn-1r=3n3n-1r=3n-n+1r=3

Since the ratio of the successive term is the non zero constant 3, therefore snis a geometric sequence with common ratio is3.

03

Step 3. To find the terms.

We have

sn=3ns1=31s1=3s2=32s2=9s3=33s3=27

and

s4=34s4=81

Thus, the first four terms are 3,9,27,81.

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