What should be added in fourth term to get the last 3 terms in AP ?

Question

The sequence k, k^2, 16, k^3 has four terms in which first three terms are in GP.
What should be added in fourth term to get the last 3 terms in AP ?

Answer 1

First 3 terms are in GP so (k^2)^2 = k*16
=> k^3 = 16
=> k = 16^1/3
For getting last 3 terms in AP, let x should be added in fourth term
so (k^2 + k^3 + x)/2 = 16
=> (k^2 + k^3 + x) = 32
=> 16^(2/3) + 16 + x = 32
=> x = 16 - 16^(2/3)