SOLUTION: the second term of a geometric is 11 and the sum to infinity is 100, find the two possible values of the common ratio and the corresponding first terms

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Question 1135595: the second term of a geometric is 11 and the sum to infinity is 100, find the two possible values of the common ratio and the corresponding first terms
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Let the first term be a and the common ratio be r. Then

(1) ar = 11 the second term is 11
(2) a/(1-r) = 100 the infinite sum is 100

Solve (1) for either variable and substitute in (2)

%2811%2Fr%29%2F%281-r%29+=+100
11%2Fr+=+100%281-r%29+=+100-100r
11+=+100r-100r%5E2
100r%5E2-100r%2B11+=+0

This is a quadratic equation that does not factor, so it has ugly irrational roots; but solving it using the quadratic formula will lead to the two solutions to the problem.