Find $p$ and $q$ such that: $2p,\ 2p+q,\ p+4q,\ 35$ are in A.P.

Given: $2p,\ 2p+q,\ p+4q,\ 35$ are in A.P.

To do: To find the value of $p$ and $q$.

Solution:

As known, $b-a=c-b$, if $a,\ b$ and $c$ are in an A.P.

$\Rightarrow 2p+q-2p=p+4q-2p-q=35-p-4q$

$\Rightarrow q=3q-p=35-p-4q$

$\Rightarrow 3q-p=q\ \Rightarrow 3q-p-q=0\ \Rightarrow p=2q$ 

And $3q-p=35-p-4q$

$\Rightarrow 35-q=0$

$\Rightarrow q=35$

$\Rightarrow p=2q=2\times35=70$

Thus, $p=70$ and $q=35$.

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Updated on: 10-Oct-2022

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