Mark the correct alternative in each of the following: In a G.P. of even number of terms, the sum of all terms is five times the sum of the odd terms. The common ratio of the G.P. is

Question

Philoid · Accepted Answer

Let,a be the first term and r be the common ratio. The

number of terms is 2n.

G.P. ⇒ a, ar, ar², …… (upto 2n terms)

Sum of all terms =

Odd terms G.P. ⇒ a, ar², ar⁴, …… (upto n terms)

Sum of odd terms G.P. =

Sum of all terms = 5×Sum of odd terms

5(1 – r) = (1 – r²)

r² – 5r + 4 = 0

(r – 1)(r – 4) = 0

r = 1(not possible) and r = 4

So, common ratio of the G.P. = 4

Mark the correct alternative in each of the following:In a G.P. of even number of terms, the sum of all terms is five times the sum of the odd terms. The common ratio of the G.P. is

Mark the correct alternative in each of the following:
In a G.P. of even number of terms, the sum of all terms is five times the sum of the odd terms. The common ratio of the G.P. is