If a, b, c be distinct, +ve and in H.P., then an + cn is

1) > bn

2) > 2bn

3) < bn

4) < 2bn

Solution: (2) > 2bn

Consider two numbers an and cn.

[an + cn] / 2 > (an cn)½

an + cn > 2 (ac)n/2 —- (i)

Also GM > HM

√ac > b

(ac)n/2 > bn —- (ii)

From (i) and (ii), [an + cn] > 2bn

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