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Chapter 12: Q 13. (page 824)

Show that each sequence is geometric. Then find the common ratio and write out the first four termsen=2n/3

Short Answer

Expert verified

The common ratio is 21/3and the first four terms are 21/3,22/3,2,24/3.

Step by step solution

01

Step 1. Given information.  

We have given sequence en=2n/3.

The localid="1646927031642" nthand (n-1)th terms are

en=2n/3en-1=2n-1/3

02

Step 2. To find the common ratio.   

We have,

r=enen-1r=2n/32n-1/3r=2n-n+13r=213

Since the ratio of the successive term is the non zero constant 213

therefore,(en)is a geometric sequence with common ratio is213.

03

Step 3. To find the terms.  

We have,

e1=213e2=223e3=233e3=2e4=243

Thus, the first four terms are213,223,2,243.

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