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Chapter 12: Q. 10 (page 816)

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

an=4-2n

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Given information 

an=4-2n

02

Step 2. Calculation 

The first term isa1=4-2路1=2.

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

an=4-2n and an-1=4-2n-1=4-2n+2=6-2n

The common difference is -

d=an-an-1=4-2n-6-2n=-2

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

The first four terms are2,0,-2,-4.

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