Question

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

Answer 1

solution:

$a_{1}=2p-1\\</p><p>a_{2}=3p+1\\</p><p>a_{3}=11\\</p><p>a_{2}-a_{1}=a_{3}-a_{2}\\</p><p>3p+1-(2p-1)=11-3p+1\\</p><p>3p+1-2p+1=11-3p+1\\</p><p>6p-2p=10\\</p><p>4p=10\\</p><p>p=\frac{10}{4}\\</p><p>p=\frac{5}{2}$

this is required answer.