In an AP, S p = q, S q = p and S r denotes the sum of first r terms. Then, S p + q is equal to

Question

Philoid · Accepted Answer

S_p = {2A + (p–1) D} = q, given

S_q = (2A + (q–1) D} = p, given

On Subtracting the second equation from 1st we get,

D = –2

Also On adding the two equations we get,

2A + = p/q + q/p

Now,

S_{p + q} = {2A + (p + q–1) D}

= {2A + (p + q–1)D}

{ + – + (p + q–1) D}

=

[ By substituting the value of D ]

= – (p + q)

In an AP, Sp = q, Sq = p and Sr denotes the sum of first r terms. Then, Sp + q is equal to