If $\frac{4}{5},\ a,\ 2$ are three consecutive terms of an A.P., then find the value of $a$.

Given: $\frac{4}{5},\ a\ and\ 2$ are three consecutive terms of an A.P.

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

Solution:

$\because \frac{4}{5},\ a\ and\ 2$ are three consecutive terms of an A.P.

 $\therefore$ Common difference $=a-\frac{4}{5}=2-a$

$\Rightarrow a+a=2+\frac{4}{5}$

$\Rightarrow 2a=\frac{10+4}{5}$

$\Rightarrow  2a=\frac{14}{5}$

$\Rightarrow a=\frac{14}{5}\times\frac{1}{2}$

$\Rightarrow a=\frac{7}{5}$

Therefore, $a=\frac{7}{5}$.
 

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Updated on: 10-Oct-2022

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