Find the value of p for which the numbers 2p – 1, 3p + 1, 11 are in AP.

Find the value of for which the numbers 2p – 1, 3+ 1, 11 are in AP. Hence, find the numbers.



$2 p-1,3 p+1,11$ are in $\mathrm{AP}$

A.P has common difference


Here, $a_{1}=2 p-1, a_{2}=3 p+1$ and $a_{3}=11$


$3 p+1-(2 p-1)=11-3 p-1$

$p+2=10-3 p$

$\Rightarrow p=2$

And the numbers are:


$\Rightarrow 3,7,11$ are the numbers



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