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Question
If the first term of a G.P. is 16 and sum of its terms to infinity is `176/5`, find the common ratio.
Solution
a = 16, sum to infinity = `176/5` …[Given]
Sum to infinity = `"a"/(1 - "r")`
∴ `176/5 = 16/(1 - "r")`
∴ `11/5 = 1/(1 - "r")`
∴ 11 – 11r = 5
∴ 11r = 6
∴ r = `6/11`.
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