# Write the first three terms of the APs when $a$ and $d$ are as given below:$a=\sqrt{2}, \quad d=\frac{1}{\sqrt{2}}$

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Given:

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

To do:

We have to write the first three terms of the given arithmetic progression.

Solution:

First term $a_1=a=\sqrt{2}$

Second term $a_2=a_1+d=\sqrt{2}+\frac{1}{\sqrt{2}}=\frac{\sqrt2 \times \sqrt2+1}{\sqrt2}=\frac{2+1}{\sqrt{2}}=\frac{3}{\sqrt{2}}$

Third term $a_3=a_2+d=\sqrt{2}+\frac{2}{\sqrt{2}}=\frac{\sqrt2 \times \sqrt2+2}{\sqrt2}=\frac{2+2}{\sqrt{2}}=\frac{4}{\sqrt{2}}$

Therefore, the first three terms of the given AP are $\sqrt{2}, \frac{3}{\sqrt{2}}, \frac{4}{\sqrt{2}}$.

Updated on 10-Oct-2022 13:27:34