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

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Solution

$\begin{matrix} W e h a v e 2 p, 2 p + q, p + 4 q, 35 a r e i n A . P \Rightarrow 2 p + q - 2 p = p + 4 q - 2 p - q \Rightarrow q = 3 q - p ∴ p = 2 q - - - - - (1) N o w, a l s o p + 4 q - 2 p - q = 35 - p - 4 q \Rightarrow 3 q - p = 35 - p - 4 q \Rightarrow 3 q - 2 q = 35 - 2 q - 41 [F r o m e q u a t i o n 1] \Rightarrow q = 35 - 6 q \Rightarrow 7 q = 35 ∴ q = 5 a n d, p = 2 q ∴ p = 10 \end{matrix}$

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