Find three arithmetic means between 6 and – 6.
Question:

Find three arithmetic means between 6 and – 6.

Solution:

let the three AM be $\mathrm{X}_{1}, \mathrm{X}_{2}, \mathrm{X}_{3}$.

So new AP will be

$6, x_{1}, x_{2}, x_{3},-6$

Also – 6 = 6 + 4d

$d=-3$

$x_{1}=3$

$x_{2}=0$

$x_{3}=-3$