SOLUTION: The third term of a g.p is 12 and the first term is 48.find the sum of the first 11 terms

Question 1205956: The third term of a g.p is 12 and the first term is 48.find the sum of the first 11 terms
Found 2 solutions by mananth, ikleyn:
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
The third term of a g.p is 12 and the first term is 48.find the sum of the first 11 terms
let a 1 be the first term,
r the common ratio,
n the term number.
The nth term of GP is tn = ar^(n-1)
third term of a G P is 12
t3 = 12 = 48 * r^2
12/48 = r^2
1/4 = r^2
r = 1/2
Sn sum of n terms of G P =

S 11 = (48*((1/2)^11 -1))/ ((1/2)-1)}},
=96 (ROUNDED OFF)

the terms are
48, 24, 12, 6, 3, 3/2, 3/4, 3/8, 3/16, 3/32, 3/64

Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.
The third term of a g.p is 12 and the first term is 48. find the sum of the first 11 terms
~~~~~~~~~~~~~~~~~~~~~~

        This problem allows two solutions :   there are two GPs satisfying the given condition,
        and they produce two different sums, i.e. two different answers.

        Thus the solution by @mananth is INCOMPLETE and, therefore, partly INCORRECT.

        I came to bring a correct solution.

For the third term of this GP, we have this equation 12 = 48*r^2. It gives r^2 = = , r = = +/- . So, there are two values for common ratio: one is r = 1/2; the other is r = -1/2. With common ratio 1/2, the sum of the first 11 terms of the GP is = = = = = 95.953125 (rounded) With common ratio -1/2, the sum of the first 11 terms of the GP is = = = = = = 32.015625 (rounded). ANSWER. Two possible answers are = 95.953125 (with r = 1/2) and = 32.015625 (with r = -1/2).

Solved.

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