$\frac{4}{5},\ a\ \frac{12}{5}$ are three consecutive terms of an A.P., find the value of $a$.

Given: $\frac{4}{5},\ a\ \frac{12}{5}$ are three consecutive terms of an A.P.

To do: To find the value of $a$.

Solution:

If $\frac{4}{5},\ a\ \frac{12}{5}$ are three consecutive terms of an A.P.

Then, $a-\frac{4}{5}=\frac{12}{5}-a$

$\Rightarrow \frac{5a-4}{5}=\frac{12-5a}{5}$

$\Rightarrow 5a-4=12-5a$

$\Rightarrow 5a+5a=12+4$

$\Rightarrow 10a=16$

$\Rightarrow a=\frac{16}{10}$

$\Rightarrow a=\frac{8}{5}$

Thus for $a=\frac{8}{5}$, $\frac{4}{5},\ a\ \frac{12}{5}$ are three consecutive terms of an A.P.

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Updated on: 10-Oct-2022

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