Question

If $6$ arithmetic means are inserted between $1$ and $\frac{9}{2}$, then find the $4^{th}$ arithmetic mean.

Answer 1

Let $a_1,a_2,a_3,a_4,a_5,a_6$ be sic arithmetic means

$\Rightarrow 1,a_1,a_2,.....,a_6,9/2$ will be in A.P.

Now,

$n^{th}$ term $a_n=a+(n-1)d$

$8^{th}$ term

$\frac{9}{2}=1+7d\Rightarrow \frac{7}{2}=7d\Rightarrow d=\frac{1}{2}$.

Hence

$4^{th}$ term

$a_4=1+4\left(\frac{1}{2}\right)=3$.