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Question

# Consider the ten numbers ar,ar2,ar3,..........ar10.If their sum is 18 and the sum of their reciprocal is 6 then the product of these ten numbers, is

A
35
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B
38
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C
310
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D
315
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Solution

## The correct option is B 35ar,ar2,ar3,............ar10 is a GP with first term as ar and common ration as r=>sum1=ar+ar2+ar3=.......ar+10=18=>sum2=1ar+1ar2+...........+1ar10=6multiply sum2 by a2r11i.e.,=>ar+ar2+ar3+..........+ar10=6×a2r11=>sum1=6a2r10=>18=6a2r10=>a2r11=3Now product of the ratio terms of the GP=>a10r1+2+3+......+10=>a10r10×11=>a10r55=(a2r11)5=>35

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