Question

find the value of p and q if 2p, 2p+q, p+4q , 35 are in ap

Answer 1

2p, 2p + q, p + 4q, 35

For this series to be in AP their common difference must be same.

(2p + q) - 2p = 35 - (p + 4q)

q = 35 - p - 4q

p = 35 - 5q. Eq1

Now put value of P in common difference

2(35 - 5q) + q = 35 - (35 - 5q + 4q)

70 - 10q + q = 35 - 35 + 5q - 4q

70 - 9q = q

70 = 10q

q = 70 / 10 = 7

Now put value of q in eq 1

p = 35 - 5(7)

p = 35 - 35 = 0

So, P = 0 and Q = 7


Thanks