Question

Check whether $-150$ is a term of the A.P. $11,8,5,2,\dots$

Answer 1

Arithmetic Progression:

Given,

A.P. $11,8,5,2.....,$

The first term, $\mathrm{a}=11$

The common difference is, $\begin{array}{rcl}\mathrm{d}& =& {\mathrm{a}}_2-{\mathrm{a}}_1\end{array}$

$\begin{array}{rcl}& =& 8-11\\ & =& -3\end{array}$

Let, ${\mathrm{n}}^{\mathrm{th}}$ the term of A.P be ${\mathrm{a}}_{\mathrm{n}}=-150$

We know that. ${\mathrm{n}}^{\mathrm{th}}$ term of A.P is given by,

$\begin{array}{rcl}{\mathrm{a}}_{\mathrm{n}}& =& \mathrm{a}+(\mathrm{n}-1)\mathrm{d}\\ -150& =& 11+(\mathrm{n}-1)(-3)\\ -150& =& 11-3\mathrm{n}+3\\ -164& =& -3\mathrm{n}\\ \mathrm{n}& =& \frac{164}{3}\end{array}$

Clearly, $\mathrm{n}$ is not an integer but a fraction.

Hence, $–150$ is not a term of this A.P.