Question

The sum of first three terms of a G.P. is 21/2 and their product is 27. Which of the following is not a term of the G.P. if the numbers are positive?

(a) 3

(b) 2/3

(c) 3/2

(d) 6

I got this question in an interview for internship.

My question is from Geometric Progression(G.P.) in portion Sequences and Series of Mathematics – Class 11

Answer 1

Correct option is (b) 2/3

To explain: 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.

Terms are 3/2, 3, 3*2 i.e. 3/2, 3, 6.