Class 11

Math

Algebra

Sequences and Series

Find three arithmetic means between $6$ and $−6$.

We know, $n_{th}$ term $T_{n}=a+(n−1)d$

$a=$ First term

$d=$ Common difference

$n=$ number of terms

$T_{n}=n_{th}$ term

Let the required AM be $x_{1},x_{2},x_{3}$. Then,

$6,x_{1},x_{2},x_{3},−6$ are in AP.

Now, $T_{5}=−6$

$⇒a+4d=−6$

$⇒6+4d=−6$

$⇒4d=−12$

$⇒d=−3$

$∴x_{1}=6+d=(6−3)=3$,

$x_{2}=6+2d=(6−6)=0$,

$x_{3}=6+3d=(6−9)=−3$.

Three arithmetic means between $6$ and $−6$ are $3,0,−3$.