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) (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)
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.
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