Find the sum of two middle most terms of the AP (-4)/3, -1, (-2)/3,......., 4 1/3

Question

Find the sum of two middle most terms of the AP \(-\frac{4}{3},-1,\frac{-2}{3},....,4\frac{1}{3}.\)

Answer 1

The given AP is \(-\frac{4}{3},-1,\frac{-2}{3},....,4\frac{1}{3}.\)

First term, \(a=-\frac{4}{3}\)

Common difference, d = \(-1-(-\frac{4}{3})\) = \(-1+\frac{4}{3}=\frac{1}{3}\)

Suppose there are n terms in the given AP. Then,

Thus, the given AP contains 18 terms. 

So, there are two middle terms in the given AP.

The middle terms of the given AP are \((\frac{18}{2})th\) terms 

and \((\frac{18}{2}+1)th\) term i.e. 9th term and 10th term.

∴ Sum of the middle most terms of the given AP

= 9^th term + 10^th term

Hence, the sum of the middle most terms of the given AP is 3.