Question

The sum of first three terms of a G.P.is 13/ 12 and their product is -1 find G.P

Answer 1

Let a/r , a and ar , are the three terms in GP.
A/C to question,
sum of three terms = 13/12
a/r + a + ar = 13/12 -----(1)

again, product of these terms = -1
a/r × a × ar = -1
a³ = -1 => a = -1

now, put a = -1 in equation (1)
-1/r + (-1) + (-1)r = 13/12
-1[ 1 + r + r²] = 13r/12
13r + 12 + 12r + 12r² = 0
12r² + 25r + 12 = 0
12r² + 16r + 9r + 12 = 0
4r(3r + 4) + 3(3r + 4) = 0
(4r + 3)(3r + 4) = 0
r = -3/4 and -4/3

so, terms are : 4/3 , -1 , 3/4 or, 3/4 , -1 , 4/3