Question

Give a very useful note on A.P. and Selection of terms of A.P.

Answer 1

$\huge \bf{Solution.}$

A very useful note on A.P

Selection of terms of an A.P.

1. When the sum of an odd number of terms in an A.P. is given, it is convenient to take the middle term as "a" and "d" as the common difference.

Thus,

(i) for three terms, we take a–d, a and a+d.

(ii) for five terms we take a–2d, a–d, a, a+d, a+2d.

2. When the sum of an even number of terms in A.P. is given, it is convenient to take the two middle terms as a–d and a+d and 2d as the common difference.

Thus,

(i) for four terms, we take

a–3d, a–d, a+d, a+3d.

(ii) for six terms, we take

a–5d, a–3d, a–d, a+d, a+3d and a+5d.