Question

If the sum of P terms of an A.P. is q and the sum of q terms is p, then the sum of p + q terms will be

 A. 0

B. p – q 

C. p + q 

D. – (p + q)

Answer 1

Let a be the first term and d is common difference of the A.P then sum of n terms in A.P is S_n = (\(\frac{n}{2}\))[ 2a + (n – 1) d] 

Here, s_p= q 

S_q = p 

Sp = (\(\frac{P}{2}\)) [2a + (p – 1) d] 

q = \(\frac{P}{2}\)[2a + (p – 1) d]

\(\frac{2q}{2}\) = [2a + (p – 1) d] --------(1)

S_q = P =\((\frac{q}{2})\)[2a + (q -1)d]

\(\frac{2P}{q}\) = [2a + (q - 1)d] .......... (2)

subtract (1) from (2) we get

(q - p)d = \((\frac{2P}{q}) - (\frac{2q}{p})\)

(q – p) d = (2p² - 2q²) / pq -----------(3) 

d = -2(q + p) / pq -----------(3) 

Sum of first (p + q) terms

[From (1) and (3)]

Answer 2

Hope you like the solution