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 RAHU SHARMA (11 years ago)

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Balakrishnan M  (11 years ago)

The sequence {A(n)} is defined by A(1)=2 and A(n+1)=A(n)+2n.
The value of 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

Is this solution Helpfull? Yes (78) | No (1)  

alok kumar pandey  (11 years ago)

here is a quicker way......
quickly find the values of n=2,3,4,5,6
we get for n=2 4
n=3 8 ( 1 less than its square i.e.9)
n=4 14 (2 less than its square i.e 16)
n=5 22 (3 less than its square i.e 25)
continuing ... for n=100 it will be 98 less than its square
so (100^2)-98=9902 ans

Is this solution Helpfull? Yes (34) | No (1)  

Lorna A. Canillo  (11 years ago)

the answer is 9,902.
a(100) = (100)(99)+2=9,902

Is this solution Helpfull? Yes (6) | No (10)  

Arif Bader  (11 years ago)

S1=2+4+8+14+22+.....upto 100terms
S1= 2+4+8 +14+22+...upto 99terms

subtracting the two series we get,
2+[2+4+6+8+.....upto 99 terms](an AP series)...
Solve it...

Is this solution Helpfull? Yes (1) | No (11)  

mageswari  (11 years ago)

let a=2 , d=2,a.p formula find nth term i.e.. tn=a+(n-1)d
where tn=100...
100=2+(n-1)2 gives n=50.
now sum of n terms n/2(a+l)=2550(ans).

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