Chapter 3.6, Problem 33HP

To determine

To determine the value of x .

Answer to Problem 33HP

  $x=-1$

Explanation of Solution

Given:

  $x+8,4x+6\&3x$ are the first three terms of an arithmetic sequence.

Concept used:

An arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

Calculation:

The difference between 2 consecutive terms of an arithmetic sequence is always equal.

So,

2^nd term − 1^st term = 3^rd term − 2^nd term

  $\begin{array}{l}(4x+6)-(x+8)=3x-(4x+6)\\ \Rightarrow 4x+6-x-8=3x-4x-6\\ \Rightarrow 3x-2=-x-6\\ \Rightarrow 3x+x=-6+2\\ \Rightarrow 4x=-4\\ \Rightarrow x=-1\end{array}$

Justification:

1^st term: $(x+8)=-1+8=7$

2^nd term: $(4x+6)=4(-1)+6=-4+6=2$

3^rd term: $3x=3(-1)=-3$

2^nd term − 1^st term = $2-7=-5$

3^rd term − 2^nd term = $-3-2=-5$

So, the difference is same.

Hence, they are the first three terms of an arithmetic sequence.

Conclusion:

The required value of x is $-1$ .