Latest TCS Aptitude Question SOLUTION: The sequence {A_n} is defined by A_1= 2 and A_(n+1)=A_n+2n. What is the value of A_100.

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The sequence {A_n} is defined by A_1= 2 and A_(n+1)=A_n+2n. What is the value of A_100.

Asked In TCS Bishal Pandey (11 years ago)

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Mohona Ghosal  (11 years ago)

A(1)=2 and A(n+1)=A(n)+2n.
A(100)=A(99+1)=A(99)+2*99
=A(98)+2*98+2*99
=A(97)+2*97+2*98+2*99

...
A(100)=A(1)+2*1+2*2+2*3+......+2*98+2*99
= 2+(2*1+2*2+2*3+......+2*98+2*99)
= 2+2(1+2+3+.....+98+99)
= 2+2(sum of the first 99 natural numbers)
= 2+2(99*100/2) [sum of the first n natural numbers={n*(n+1)/2}]
= 2+9900
= 9902

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way  (11 years ago)

9902 is the answer

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Sri Reddy  (10 years ago)

A100=2+n(n-1)
here n is 100
soo by keeping n=100 we get 9902

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