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

Given: $k\ +\ 9,\ 2k\ –\ 1$ and $2k\ +\ 7$ are the consecutive terms of an A.P.

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

If $k\ +\ 9,\ 2k\ –\ 1$ and $2k\ +\ 7$ are the consecutive terms of A.P., then the common difference will be the same.

$\therefore \ ( 2k\ –\ 1) \ –\ ( k\ +\ 9) \ =\ ( 2k\ +\ 7) \ –\ ( 2k\ –\ 1)$

$\therefore \ k\ –\ 10\ =\ 8$

$\therefore \ k\ =\ 18$