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Question

Consider 10 numbers ar,ar2,ar3,....,ar10. Their sum is 18 and the sum of their reciprocal is 6. If the product of these 10 numbers is ab (where a and b are prime) then find the value of a+b.

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Solution

Given
ar+ar2+ar3+......ar10=18 …………..(1)
1ar+1ar2+.....1ar10=6 ………..(2)
From (2)
(r9+r8+.....1)ar10=6
ar(r9+r8+......1)ar(ar10)=6
ar10+ar9+....ara2r11=6
/183a2r11=/6
a2r11=3
Product of 10 numbers =(ar)(ar2)(ar3).(ar10)
=a10r(1+2....10)=a10r55
=(a2r11)535
The value of a+b=3+5=8.

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