Q4. If  x 1 ,   x 2 . . . . . . . . . ,   x n   a n d   1 h 1 ,   1 h 2 , . . . . . . . . .   , 1 h n   are two A.P.s such that x3 = h2 = 8 and x8 = h7 = 20, then x5.h10 equals
(A) 2560            (B) 2650                (C) 3200                (D) 1600

Let common difference of first A.P. be d and that of second be Dx3=x1+3-1d=x1+2d8=x1+2d _____1x8=x1+8-1d=x1+7d20=x1+7d ______21h2=1h1+2-1D=1h1+D18=1h1+D ________31h7=1h1+7-1D=1h1+6D120=1h1+6D _________4Subtract equation 1 from 212=5dd=125Put in equation 18=x1+245x1=165Subtract equation 3 from 4120-18=5D-340=5DD=-3200Put in equation 318=1h1-32001h1=25+3200=28200=750x5=x1+5-1d=x1+4d=165+485=6451h10=1h1+10-1D=1h1+9D=750-27200=28-27200=1200h10=200x5.h10=200×645=40×64=2560

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