prove that the sum of first 6 terms in a g p is a (1+r) (1+r2+r4) - Maths - Sequence and Series of Real Numbers

Question

prove that the sum of first 6 terms in a g p is a (1+r)
(1+r2+r4)

Pradeep Krishna · Answer

sum of first 6 terms is
a+ar+ar2+ar3+ar4+ar5
​we shall do a small trick to this
a+ar2+ar4+ar+ar3+ar5
​=a(1+r2+r4)+ar(1+r2+r4)
=a+ar(1+r2+r4)
​=a(1+r)(1+r2+r4)

prove that the sum of first 6 terms in a g.p is a (1+r) (1+r2+r4).

prove that the sum of first 6 terms in a g.p is a (1+r) (1+r²+r⁴).