Question

Write the first three terms of the $\mathrm{AP}$ when $a$ and $d$ are as given below: $a=\frac{1}{2},d=\frac{-1}{6}$

Answer 1

First Three terms of $\mathrm{AP}$.

The first three terms of AP can be expressed as :

$a,a+d,a+2d$

So,

$\begin{array}{rcl}& \Rightarrow & a=\frac{1}{2}\\ & \Rightarrow & a+d=\frac{1}{2}+\left(\frac{-1}{6}\right)\\ & =& \frac{1}{2}-\frac{1}{6}\\ & =& \frac{3-1}{6}\\ & =& \frac{2}{6}\\ & =& \frac{1}{3}\\ & \Rightarrow & a+2d=\frac{1}{2}+2\left(\frac{-1}{6}\right)\\ & =& \frac{1}{2}-\frac{1}{3}\\ & =& \frac{3-2}{6}\\ & =& \frac{1}{6}\end{array}$

Hence, the first three terms of the given arithmetic progression are $\frac{1}{2},\frac{1}{3}$ and $\frac{1}{6}$.