Question

The sum of the first three terms of a G.p is half its sum to infinity.find the positive common ratio

Answer 1

Sum of infinite terms of GP suggests common ratio r < 1.

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

a + ar + ar² = a/2(1 - r)

=> r² + r + 1 = 1/2(1 - r)

=> r² + r + 1 - r³ - r² - r = 1/2

=> r³ = 1/2

=> r = (½)^⅓

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