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) 6I 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

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

1.	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) 6I 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» Correct option is (b) 2/3 To explain: LET THREE terms be a/R, a, ar. Product = 27 => (a/r) (a) (ar) = 27 => a^3 = 27 =>a = 3. Sum = 21/2 => (a / r + a + ar) = 21/2 => a (1 / r + 1 + 1r) = 21/2 => (1 / r + 1 + 1r) = (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, 32 i.e. 3/2, 3, 6.

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