Question

Write the first three terms of the $\mathrm{APs}$ when $a$ and $d$ are as given below:$\left(3\right)a=\sqrt{2},d=\frac{1}{\sqrt{2}}$

Answer 1

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

The first three terms of $\mathrm{AP}$ can be expressed as :

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

Here, $a=\sqrt{2},d=\frac{1}{\sqrt{2}}$

$$\begin{gathered} \Rightarrow a=\sqrt{2} \\ \Rightarrow a+d=\sqrt{2}+\frac{1}{\sqrt{2}} \\ =\frac{3}{\sqrt{2}} \\ \Rightarrow a+2d=\sqrt{2}+\frac{2}{\sqrt{2}} \\ =\frac{4}{\sqrt{2}} \end{gathered}$$

Hence, the first three terms of the given arithmetic progression are $\sqrt{2},\frac{3}{\sqrt{2}},\frac{4}{\sqrt{2}}$.