Question

If the numbers p-1, 2p and 3p+1 are in A.P., find the value of p.

Answer 1

we know that for findind the value of p we have to find a and d
for a=p-1(given)
d=a2-a1
so , 2p-(p-1)
2p-p+1, p+1
so d=p+1
for finding p
a2=a+d
p-1+p+1, 2p+0, p=-2
for proving it
put value of p
in a=p-1
-2-1=-3
2)2p= 2.(-2)=-4
so for check it
d=a2-a1
-4-(-3)
-1