Answer :

Let T indicate a term of the progression.
T1, T2, T3, ..., Tn, ...T2n
T1 = 1
T2 = a
T3 = ca
T4 = c.a2
T5 = c2.a2
Tk if k is even =


T2n =


T2n =


S2n = 1 + a + ca + c.a2 + c2.a2 + c2.a3 .....an. cn - 1
= 1 + [ a + c.a2 + c2.a3.... + an.cn - 1 ] + [ ca + c2.a2 + c3.a3..... + cn - 1.an - 1]
The sum of a G.P. =


For a + c.a2 + c2.a3.... + an.cn - 1


a = a, r = ca, n = n



For [ ca + c2.a2 + c3.a3..... + cn - 1.an - 1]


a = ca, r = ca, n = n



The required result



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