Question

For what value of $k$ will $k+9$,$2k-1$ and $2k+7$ be the consecutive terms of an A.P?

Answer 1

Calculate $k$ using conditions of AP:

If $k+9$,$2k-1$ and $2k+7$ are the consecutive terms of an A.P, then the common difference ‘$d$’ will be the same.

Therefore,

$(2k-1)-(k+9)=(2k+7)-(2k-1)$

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

$\Rightarrow$ $k-10=7+1$

$\Rightarrow$ $k=10+8$

$\Rightarrow$ $k=18$

Hence, if $k=18$, the consecutive terms $k+9$,$2k-1$ and $2k+7$ are in AP.