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Question

# Consider the ten numbersar,ar2,ar3,....ar10If their sum is 18 and the sum of their reciprocals is 6 then the product of these ten numbers ,is:

A
324
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B
343
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C
243
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D
729
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Solution

## The correct option is C 243Given numbers are ar,ar2,ar3,...,ar10Given sum of the numbers =18⇒ar+ar2+ar3+...+ar10=18⇒ar(1+r+r2+...+r9)=18 .........(1)Given sum of their reciprocals is 6,⇒1ar+1ar2+...+1ar10=6⇒1ar10(1+r+r2+...+r9)=6 ........(2)Dividing equation(1) by (2), we get a2r11=3Product of these ten numbers,a×ar×ar2×ar3×...×ar10=a10r55=(a2r11)5=35=243

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