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Question

Consider the ten numbers
ar,ar2,ar3,....ar10
If 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 243
Given numbers are ar,ar2,ar3,...,ar10
Given 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=3
Product of these ten numbers,
a×ar×ar2×ar3×...×ar10
=a10r55
=(a2r11)5
=35=243

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