Question

The sum of first three terms of a G.P. is 21/2 and their product is 27. Find the common ratio.

(a) 2

(b) 1/2

(c) 2 or 1/2

(d) neither 2 nor 1/2

This question was addressed to me in unit test.

Enquiry is from Geometric Progression(G.P.) topic in section Sequences and Series of Mathematics – Class 11

Answer 1

Right option is (c) 2 or 1/2

Explanation: Let three terms be a/r, a, a*r.

Product = 27 => (a/r) (a) (a*r) = 27 => a^3 = 27

=>a = 3.

Sum = 21/2 => (a / r + a + a*r) = 21/2 => a (1 / r + 1 + 1*r) = 21/2

=> (1 / r + 1 + 1*r) = (21/2)/3 = 7/2

=> (r^2 + r + 1) = (7/2) r => r^2 – (5/2) r + 1 = 0

=> r = 2 and 1/2.