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If f n + 1 = 2 f n + 1 2 for n = 1 , 2 , 3 … … . . and f 1 = 2 , then f 101 10 is equal to

Correct answer

5.2

Step-by-step solution

f n + 1 = f n + 1 2 ⇒ f n + 1 - f n = 1 2 ⇒ f 1 , f 2 , f 3 … … . . are in AP with common difference 1 2 . f 101 = f 1 + 100 d = 2 + 100 × 1 2 = 52 ⇒ f 101 10 = 5.2

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