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Chapter 12: Q 11. (page 824)

Show that each sequence is geometric. Then find the common ratio and write out the first four terms cn=2n-14.

Short Answer

Expert verified

The common ratio is 2and the first four terms are 14,12,1,2.

Step by step solution

01

Step 1. Write the given information.

We have given sequence.

cn=2n-14

The nth and (n-1)th term are

cn=2n-14cn-1=2(n-1)-14cn-1=2n-24
02

Step 2. To find the common ratio. 

We have,

r=cncn-1r=2n-142n-24r=2n-1-n+2r=2

Since the ratio of the successive term is the non zero constant 2, therefore cnis a geometric sequence with common ratio is 2.

03

Step 3. To find the terms. 

We have,

c1=21-14c1=14c2=22-14c2=24c2=12c3=23-14c3=44c3=1c4=24-14c4=84c4=2

Thus, the first four terms are14,12,1,2

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