Home
Class 12
MATHS
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 idexed numbers is `3018`, what is the sum of all numbers ?

A

`0`

B

`9054`

C

`12072`

D

`6036`

Text Solution

Verified by Experts

The correct Answer is:
D
`(d)` `a_(2)=(a_(1)+a_(2))/(2)`
`a_(3)=(a_(2)+a_(4))/(2)`
`a_(1)=(a_(2)+a_(2012))/(2)`
`a_(2012)=(a_(2001)+a_(1))/(2)`
Now `a_(2)+a_(4)+…+a_(2012)=3018`…….`(i)`
`2a_(2)+2a_(4)+..+2a_(2012)=6036`
`:.a_(1)+a_(2)+a_(3)+a_(5)+...+a_(2011)+a_(1)=6036`
`:.2(a_(1)+a_(3)+...+a_(2011))=6036`
`:.a_(1)+a_(3)+...+a_(2011)=3018`.........`(ii)`
By adding `(i)` and `(ii)` we get
`a_(1)+a_(2)+a_(3)+...+a_(2012)=6036`
Promotional Banner

Topper's Solved these Questions

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise Comprehension|7 Videos

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|4 Videos

  • PROBABILITY II

    CENGAGE PUBLICATION|Exercise MULTIPLE CORRECT ANSWER TYPE|6 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|3 Videos

Similar Questions

Explore conceptually related problems

Four different integers form an increasing A.P. One of these numbers is equal to the sum of the squares of the other three numbers. Then The sum of all the four numbers is -

Four different integers form an increasing A.P. One of these numbers is equal to the sum of the squares of the other three numbers. Then The product of all numbers is -

The L.C.M of two numbers is 150 and their ratio is 2:3.The sum of the two numbers will be

Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.

If a_(1),a_(2),a_(3),a_(4),...,a_(n) are n positive real numbers whose product is a fixed number c, then the minimum value of a_(1)+ a_(2) + ...+a_(n-1)+2a_(n) is-

Two dice thrown simultaneously. What is the probability that the first dice give even number and sum of two numbers is 8?

How many numbers of four digits can be formed from the numbers 1,2,3,4 ? Find the sum of all such numbers (the digits are to be used once only ).

Find the sum of all possible products of first n natural numbers taken two by two.

What is the probability that a number selected from the numbers 1,2,3….25 is prime number when each of the given numbers is equally likely to be selected?

Find the sum of all the numbers of the form n^(3) lying between 100 and 10,000.