Latest others Aptitude Question SOLUTION: . The sequence {An} is defined by A1 = 2 and An+1=An+2n what is the value of A100

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(#M40038649) OTHERS Numerical Ability question Keep an EYE

. The sequence {An} is defined by A1 = 2 and An+1=An+2n what is the value of A100

Asked In others sowjanya (9 years ago)

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Rajat sadhu  (9 years ago)

A1=2,A2=4,A3=8,A4=14........
each term is incremented by 2n ie
1st increment is of 2,then 2nd is 4 then 3rd is of 6 and so on
so the incement in the terms follows the series 2,4,6,.......198(for 99th term)
summation of the A.P. series=990
hence A100 will be incremented by 990 from A1 i.e.
A100=A1+990=992

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kiruthiga  (9 years ago)

A1=2
A2=A1+1=A1+2=2+2=4
A3=A2+1=A2+4=4+4=8
So the first few terms are 2,4,8,14,22......
the differences of the above terms are 2,4,6,8,10....
and the differences of difference are 2,2,2,2 all are equal. So this series represents a quadratic equation
Assume An=an^2+bn+c
Now A1=A+b+c=2
A2=4a+2b+c=4
A3=9a+3b+c=8
Solving we get a=1,b=-1,c=2
Substituting in An:n^2-n+2
Substitute 100 in above equation we get 9902
Ans:9902

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