Question

The sum of 1st 3 terms of a g.p. is 13/12 and their product is -1.find the terms.

Answer 1

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Answer 2

Let the g.p be
a/r , a , ar. .........(1)
so according to question

a/r + a +ar =13/12. .........(2)

(a/r)*(a)*(ar) = -1. .........(3)

so by eqn (3) cancel the r and we get
a^3 = -1
a = -1

putting the value of a in eqn (2) we have

(-1/r) + (-1) + (-r) = 13/12

by taking LCM we get
(-1 - r - r^2)/r = 13/12

(-1 - r - r^2)*12 = 13r. (cross multiply)

-12 - 12r - 12 r^2 = 13r

12r^2 + 25r + 12 = 0

12r^2 + (16+9)r + 12 = 0

12r^2 + 16r + 9r + 12 = 0

4r(3r +4) + 3(3r + 4) = 0

(3r + 4)(4r + 3) = 0

so we get

r = -4/3 , r = -3/4

putting the value of a and r in equation (1)
we get the gp and the gp is
4/3 , -1 , 3/4

or

3/4 , -1 , 4/3

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