Question

The fourth power of the common difference of an A.P with integer entries is added to the product of any four consecutive terms of it, resulting sum is

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

If d is the common difference of the A.P. the four terms are a, a + d, a + 2d, a + 3d $\therefore d^4+a(a+d)(a+2d)(a+3d)=d^4+6a^{3}d+11a^2{d}^2+6a{d}^3+a^4$
$=(a^2+3ad+d^2{)}^2$