Question

Find the value of middle term of an A.P -11, -7,-3................49.

Answer 1

Given series :-

$-11,-7,-3...49.$

Common Difference :- $-7+11=4$.

Now $a_n=49=-11+(n-1)4$

$60=(n-1)1$

$\Rightarrow 15+1=n$

$\Rightarrow n=16$

since $n$ is even there are two middle terms ${\frac{n}{2}}^{th}$ term and ${(\frac{n}{2}+1)}^{th}$ term

Now middle term will be $8^{th}$ and $9^{th}$ term

$a_8=-11+7\left(4\right)=-11+28=17$

$a_9=-11+8\left(4\right)=-11+32=21$