The middle term of the series

4 + 6 + 8 + ....... + 196 is

100

The correct answer is Option (3) → 100

First term $a=4$

Common difference $d=6−4=2$

Last term $l=196$

Formula for the nth term of an A.P.:

$a_n=a+(n−1)d$

Substitute values:

$196=4+(n−1)×2$

$196 - 4 = 2(n - 1)$

$192=2n−2$

$194=2n$

$n=97$

Since there are 97 terms, the middle term is the 49th term (because the middle of 97 = (97 + 1)/2 = 49th).

$T_{49} = a + (49 - 1)d$

$T_{49}=4+48×2$

$T_{49}=4+96=100$

The middle term is 100