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Suppose a(1),a(2),a(3),……,a(2012) are in...

Suppose `a_(1),a_(2),a_(3),……,a_(2012)` are integers arranged on a circle. Each number is equal to the average of its two adjacent numbers. If the sum of all even indexed numbers is 3018, what is the sum of all numbers ?

A

0

B

1509

C

3018

D

6036

Text Solution

Verified by Experts

The correct Answer is:
D
`a_(1),a_(2),a_(3)……,a_(2012)=3018…………….(1)`
`(a_(1)+a_(3))/(2)=a_(2)`
`2a_(2)+2a_(4)+2a_(6)+.....+2a_(2012)=6036`
`(a_(1)+a_(3))+(a_(3)+a_(5))+(a_(5)+a_(7))+....+(a_(2011)+a_(1))=6036`
`2(a_(1)+a_(3)+a_(5)+.....+a_(2011))=6036`
`a_(1)+a_(3)+a_(5)+.....+a_(2011)=3018...............(2)`
Add (1) and (2)
Sum of all number `=3018+3018=6036`
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