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Question:

If x1, x2, ..., xn and 1/h1, 1/h2, ..., 1/hn are two A.P.s such that x3 = h2 = 8 and x8 = h7 = 20, then x5 * h10 equals.

2650

3200

1600

2560

Solution:

Letd1be the common difference of the A.P.x1,x2,..., thenx8−x3=5d1=12⇒d1=125=2.4⇒x5=x3+2d1=8+2×125=12.8Letd2be the common difference of the other sequence then5d2=120󔼚=�⇒d2=�⇒1h10=1h7+3d2=1200⇒h10=200⇒x5⋅h10=12.8×200=2560So option A is the correct answer.