Question

Find p and q such that 2p, 2p + q , p + 4q , 35 are in AP.

Answer 1

this is easy
try by using R D Sharma guide

Answer 2

given the no.s are AP
2p+q-2p=35-p-4q
5q=35-p
p+5q=35▪▪▪▪▪▪1✴(equation 1)

in an AP twice of second term is equal to sum of first and third term

➡️2(2p+q)=p+4q+2p
4p+2q=3p+4q
p=2q
from equation 1
2q+5q=35
7q=35
q=5
and p=10