Question

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

Answer 1

$\because$ $2p-1,3p+1,11$ are in A.P.,

$(3p+1)-(2p-1)=11-(3p+1)\Rightarrow p+2=-3p+10\Rightarrow 4p=8\therefore p=2$

So, the numbers are $2p-1=2\times 2-1=3$, $3p+1=3\times 2+1=7$ and $11$.