Question

For what value of $KK+9,2K-12K+7$ are consecutive terms of ap

Answer 1

Here,

$a_1=K+9$

$a_2=2K-1$

$a_3=2K+7$

Common difference is $d$.

If they are in $AP$ then $d$ will be same throughout.

$\therefore$ $a_2-a_1=a_3-a_2$

$\Rightarrow$ $(2K-1)-(K+9)=(2K+7)-(2K-1)$

$\Rightarrow$ $2K-1-K-9=2K+7-2K+1$

$\Rightarrow$ $K-10=8$

$\therefore$ $K=18$

$\therefore$ Value of $K$ is $18$.