Question

If $\frac{6}{5},$ $a,4$ are in AP, the value of $a$ is

• A. $1$
• B. $13$
• C. $\frac{13}{5}$
• D. $\frac{26}{5}$

Answer 1

Answer: (C)

$\frac{13}{5}$

Given, $\frac{6}{5},a,4$ are in AP
If $a_1,a_2,a_3$ are in AP, the common difference will be the same

$\Rightarrow d=a_2-a_1=a_3-a_2$
For the given terms: $\frac{6}{5},a,4$

$\therefore$ $d=a-\frac{6}{5}=4-a$

$\Rightarrow$ $2a=\frac{6}{5}+4$

$\Rightarrow$ $2a=\frac{6+20}{5}$

$\Rightarrow$ $a=\frac{26}{10}$
$=\frac{13}{5}$