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Chapter 12: Q. 9 (page 816)

In the problem, show that each sequence is arithmetic. Find the common difference and write out the first four terms.

cn=6-2n

Short Answer

Expert verified

The solution is d=-2; first four terms=4,2,0,-2.

Step by step solution

01

Step 1. Given information 

cn=6-2n

02

Step 2. Calculation 

The first term is c1=6-2路1=4.

The nth term and the n-1st term of the sequence are-

cn=6-2n and cn-1=6-2n-1=6-2n+2=8-2n

The common difference is -

d=cn-cn-1=6-2n-8-2n=-2

Since the difference of any two successive terms is the constant -2, the sequence cnis arithmetic.

The first four terms are4,2,0,-2.

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