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Chapter 12: Q. 55 (page 817)

Find x so that x + 3, 2x + 1, and 5x + 2 are consecutive terms of an arithmetic sequence.

Short Answer

Expert verified

The value of x is-32

Step by step solution

01

Given Information 

x + 3, 2x + 1, and 5x + 2 are consecutive terms of an arithmetic sequence

02

common difference 

a1=x+3a2=2x+1a3=5x+2a2-a1=2x+1-(x+3)=x-2a3-a2=5x+2-(2x+1)=3x+1

03

 common difference is a constant 

common difference is constant in arithmetic sequence

a2-a1=a3-a2x-2=3x+1x-3x-2=1-2x-2=1-2x=1+2-2x=3x=-32thevalueofx=-32

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