Question

The sum of first three terms of a g.P is 13/12 and their product is -1.Find the first term,common ratio and the terms

Answer 1

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Answer 2

Let us assume that the values are a/p, a, ap which are in geometric progression with common ratio p. Now, we have, the sum of these values be 13/12 i.e.

a/p + a + ap = 13/12

or, a* (p+ 1+ 1/p) = 13/12..................................................(1)

Again, we have, product of these values be -1. i.e.

ap* a* a/p = -1

or, a^3 = -1

or, a = -1

Replacing the value of "a" in (1), we have

p+ 1+ 1/p = -13/12

or, p^2 +p +1 = -13p/12

or, 12p^2 + 25p + 12 = 0

or, (4p + 3)(3p + 4) = 0

or, p = -3/4 or, -4/3

Now we have the values of a and p.so, we have values 3/4, -1, 4/3.

Answer:

(1) First term is 3/4.

(2) Common ratio is either -3/4 or -4/3. whatever we take the common ratio, the terms will remain constants.

(3) The terms are 3/4, -1 , 4/3.