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Chapter 12: Q 12. (page 824)

Show that each sequence is geometric. Then find the common ratio and write out the first four termsdn=3n9.

Short Answer

Expert verified

The common ratio is 3 and the first four terms are13,1,3,9.

Step by step solution

01

Step 1. Given information. 

We have given sequence dn=3n9

The nthand (n-1)thterms are

dn=3n9dn-1=3n-19

02

Step 2. To find the common ratio.  

We have,

r=dndn-1r=39n3n-19r=3n-n+1r=3

Since the ratio of the successive term is the non zero constant3, thereforedn is a geometric sequence with common ratio is3.

03

Step 3. To find the terms. 

We have,

d1=319d1=13d2=329d2=1d3=339d3=3d4=349d4=9

Thus, the first four terms are13,1,3,9.

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Most popular questions from this chapter

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

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