a_n = a * r^(n - 1)

a : initial term of an geometric progression

r : common ratio of successive members

a_n : the nth term of the sequence

For the geometric progression, 2, 14, 98, 686, 4802, we have

(2 + 14 + 98 + 686 + 4802)(2 - 14 + 98 - 686 + 4802)

= 2^2 + 14^2 + 98^2 + 686^2 + 4802^2

Prove that infinitely many geometric progressions have this property.

Prove that infinitely many geometric progressions have this property.

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