Question

For what value of "k" will the consecutive terms 2k+1,3k+3 and 5k-1 from an A.P?

Answer 1

if these are in AP then

3k + 3 - 2k - 1 = 5k - 1 - 3k - 3
k + 2 = 2k - 4
k = 6

Answer 2

since a₂-a₁ = a₃-a₂

So, 3k+3-2k-1 = 5k-1-3k-3
       k+2 = 2k-4
       k-2k = -4-2
        -k  =  -6 
k  = 6