$\frac{4}{5},\ a\ \frac{12}{5}$ 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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