for what values of k , the numbers 1+k , 5/6+k , 13/18+k are in GP

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Solution

By using property of GP,
b²=ac
(5/6 + k)² = (1+k ) (13/18 +k )

25 /36 + k² + 10 /6 k = 13/18 + k + 13/18 k + k²

13/18 k + k - 10/6 k = 25/36 -13/18

k / 18 = - 1/36

k = - 1/2

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