Latest TCS Aptitude Question SOLUTION: The sequence {An} is defined by A1=2 and An+1=An +2n what is the value of A(100). a. 9900 b. 9902 c. 9910 d. 9916

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The sequence {An} is defined by A1=2 and An+1=An +2n what is the value of A(100).

a. 9900
b. 9902
c. 9910
d. 9916

Asked In TCS shikha panwar (9 years ago)

Unsolved Read Solution (7)

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Read Solution (7) :

Conan  (9 years ago)

given A(n) = 2,A(n+1) = A(n) + 2n

consider A(2) = A(1) + (2)

A(3) = A(2) + 4 => A(3) = A(1) + (2+4)

Similarly

A(4) = A(1) + (2+4+6)

A(100) = A(1) + (2+4+6+.....+198)
A(100) = 2 + (sum up to 99 terms)
A(100) = 9902

Is this solution Helpfull? Yes (13) | No   

ponugubati bharathi  (9 years ago)

We know that A1 = 2 so A1+1=A2=4,A3=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 differences are 2, 2, 2, 2. all are equal. so this series represents a quadratic
equation.
Assume An=an2+bn+c
Now A1 = a + b + c = 2
A2= 4a + 2b + c = 4
A3= 9a + 3b + c = 8
Solving above equations we get a = 1, b = - 1 and C = 2
So substituting inAn =n2+bn+c =n2-n+2
Substitute 100 in the above equation we get 9902.

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RAVI VERMA  (9 years ago)

A(1)=2
A(2)=A(1)+(1*2)
A(3)=A(1)+(2*3)
A(4)=A(1)+(3*4)
...............
A(100)=A(1)+(99*100)=9902

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abhisek banerjee  (9 years ago)

question is unclear.should be like A(n+1)=A(n)+2n

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ANKIT SHARMA  (9 years ago)

9902
The series is 2,4,6,8.....99terms. Sum=9900. ans=9900+2=9902

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kalpana kumari  (9 years ago)

in q A1=2 &An+1=An+2n
A2=A1+2
A3=A2+4=A1+2+4=A1+6
A4=A1+2+4+6
SIMILAR
A100=A1+2+4+6.......198=A1+2(1+2+3......99)
in ap series
A1+2((99*100)/2)=A1+9900
9902

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Aritra Das  (9 years ago)

a1=2
a2=4
a3=8
a4=14
so difference between them are 2 4 6 like this i.e. in ap
so a100=a1+sum of 99 terms of that ap
a100=2+9900
9902

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