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Question
If the first term of the G.P. is 16 and its sum to infinity is `96/17` find the common ratio.
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Solution
Given:
First term, a = 16
Sum to infinity, S∞ = `96/17`
Formula for sum to infinity of a G.P.:
`S_∞ = a/(1-r)`, where ∣r∣ < 1
`96/17 = 16/(1-r)`
96(1 − r) = 17 × 16
96 − 96r = 272
−96r = 272 − 96
−96r = 176
`r = -176/96`
`= -11/6`
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