Consider the ten numbers ar,ar2,ar3,.........,ar10ar,ar2,ar3,.........,ar10. If their sum is 18 and the sum of their reciprocals is 6 then the product of these ten numbers, is
Answers
Answer:
243
Step-by-step explanation:
Given numbers are ar, ar²,ar³......,ar¹⁰.
Given sum of the numbers = 18,
=> ar + ar²+......+ar¹⁰ = 18
=>ar(1 + r +.....+r⁹) = 18-----(1)
Given sum of their reciprocals is 6,
=> 1/ar + 1/ar² +.....+1/ar¹⁰=6,
=>1/ar¹⁰(1 + r +.....+r⁹)=6----(2)
Dividing equation(1) by (2), we get a²r¹¹ = 3-----(*)
Product of these ten numbers,
= a×ar×......×ar¹⁰ = a¹⁰r⁵⁵ = (a²r¹¹)⁵
= 3⁵ = 243.
Answer:
Given numbers are ar, ar²,ar³......,ar¹⁰.
Given sum of the numbers = 18,
=> ar + ar²+......+ar¹⁰ = 18
=>ar(1 + r +.....+r⁹) = 18-----(1)
Given sum of their reciprocals is 6,
=> 1/ar + 1/ar² +.....+1/ar¹⁰=6,
=>1/ar¹⁰(1 + r +.....+r⁹)=6----(2)
Dividing equation(1) by (2), we get a²r¹¹ = 3-----(*)
Product of these ten numbers,
= a×ar×......×ar¹⁰ = a¹⁰r⁵⁵ = (a²r¹¹)⁵
= 3⁵
Step-by-step explanation: