Q12 of 24 Page 115

Determine k so that 2/3, k and 5k/8 are the three consecutive terms of an A.P.

If x, y and z are in AP, the differences between consecutive terms will be same


⇒ y – x = z – y


⇒ 2y = x + z


As, , k and are the three terms in AP




⇒ 48k2 = 16k + 15


⇒ 48k2 – 16k – 15 = 0


⇒ 48k2 – 36k + 20k – 15 = 0


⇒ 12k(4k – 3) + 5(4k – 3) = 0


⇒ (12k + 5)(4k – 3) = 0


⇒ 12k + 5 = 0 or 4k – 3 = 0


⇒ or


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