Question

If 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. Prove that the resulting sum is the square of an integer.

Answer 1

Let AP is 2,4,6,8,10,12, ......

common difference (D) = 4-2=6-4=8-6= 2

ATQ
(According to Question)
we have to prove

D^4 + (Product of any four term of AP) =
square of an integer


2^4 + (2×4×6×8)

=16 + 384
=400

400 is square of 20 thus it is proved.

Answer 2

Here is ur answer ⤴⤴

Hope it helps u ❤