Question

Find the middle term of the AP 6, 13, 20, ...., 216.

Answer 1

A=6
d=7
$a_n=a+(n-1)d$
216=6+(n-1)$\times$ 7
n=31
total no. of terms = 31
middle term = $\frac{31+1}{2}$
=16th
$T_{16}=a+(16-1)d$

$=6+(15\times 7)=111$

therefore the middle term of the AP is 111