Latest TCS Aptitude Question SOLUTION: The sequence {A(n)} is defined by A1=2 and A(n+1)=A(n)+2n. what is the value of A(100)? a)9902 b)9900 c)10100 d)9904

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(#M40010719) TCS Numerical Ability question Keep an EYE

The sequence {A(n)} is defined by A1=2 and A(n+1)=A(n)+2n.
what is the value of A(100)?
a)9902
b)9900
c)10100
d)9904

Asked In TCS krishnaprasad TATA (11 years ago)

Unsolved Read Solution (9)

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Read Solution (9) :

Nandhini  (11 years ago)

Given A1 = 2
An+1 = An + 2n
Next number in the sequence will be,
A2 = A1 + 2*1 which can be written as,
A2 – A1 = 2*1  eqn.1
A3 – A2 = 2*2  eqn.2
A4 – A3 = 2*3  eqn.3
and so on till,
A100 – A99 = 2*99  eqn.99
By adding all the above eqns. we get,
A100 – A1 = 2*(1+2+3+4+……… + 99)
(using sum of n integers formula = n * (n+1)/2)
n=99
A100 – A1 = 2 * [99 * (99 + 1)] / 2
A100 – A1 = 99 * 100
A100 – A1 = 9900
A100 = 9900 + 2 = 9902

Is this solution Helpfull? Yes (117) | No (12)  

shashank mishra  (9 years ago)

Given A1 = 2
An+1 = An + 2n
Next number in the sequence will be,
A1=2 or
A2=A1+2*1=4 or 2*1+2=4
A3=A2+2*2=8 or 3*2+2=8
A4=A3+2*3=14 or 4*3+2=14
A5=A4+2*4=22 or 5*4+2=22
.......................
simply,
we have to find A100
so 100*99+2=9902

Is this solution Helpfull? Yes (23) | No   

Mukesh Yadav  (11 years ago)

A1=2
A2=A1+2*1=4
A3=A2+2*2=8
A4=A3+2*3=14
A5=A4+2*4=22
A6=A5+2*5=32………..A99=A98+2*98, A100=A99+2*99
By adding all the above equations, we get
A1+A2+……+A99+A100 = (A1+A2+…..+A99)+2(1+2+3+4+…….99)
Cancelling L.H.S. with R.H.S.(A1 to A99 gets cancelled), We get
A100=2*(1+2+3+…..+99)
Using sum of n integers formula = n * (n+1)/2) where , n=99
A100= 2 * [99 * (99 + 1)] / 2
A100 = 99 * 100
A100 = 9900
Answer: 9900

Is this solution Helpfull? Yes (17) | No (24)  

srikanthreddy karnati  (11 years ago)

Given A1 = 2
An+1 = An + 2n
Next number in the sequence will be,
A2 = A1 + 2*1 which can be written as,
A2 – A1 = 2*1 ïƒ eqn.1
A3 – A2 = 2*2 ïƒ eqn.2
A4 – A3 = 2*3 ïƒ eqn.3
and so on till,
A100 – A99 = 2*99 ïƒ eqn.99
By adding all the above eqns. we get,
A100 – A1 = 2*(1+2+3+4+……… + 99)
(using sum of n integers formula = n * (n+1)/2)
n=99
A100 – A1 = 2 * [99 * (99 + 1)] / 2
A100 – A1 = 99 * 100
A100 – A1 = 9900
A100 = 9900 + 2 = 9902

Is this solution Helpfull? Yes (6) | No (3)  

piyushkumar  (11 years ago)

its b 9900
A1 = 2
An+1 = An + 2n
Next number in the sequence will be,
A2 = A1 + 2*1 which can be written as,
A2 – A1 = 2*1  eqn.1
A3 – A2 = 2*2  eqn.2
A4 – A3 = 2*3  eqn.3
and so on till,
A100 – A99 = 2*99  eqn.99
By adding all the above eqns. we get,
A100= 2*(1+2+3+4+……… + 99)
(using sum of n integers formula = n * (n+1)/2)
n=99
A100 = 2 * [99 * (99 + 1)] / 2
A100 = 9900

Is this solution Helpfull? Yes (4) | No (17)  

harish  (8 years ago)

A1=2
A2=A1+2*1=4
A3=A2+2*2=8
A4=A3+2*3=14
A5=A4+2*4=22
A6=A5+2*5=32………..A99=A98+2*98, A100=A99+2*99
By adding all the above equations, we get
A1+A2+……+A99+A100 = 2+((A1+A2+…..+A99)+2(1+2+3+4+…….99))
Cancelling L.H.S. with R.H.S.(A1 to A99 gets cancelled), We get
A100=2+2*(1+2+3+…..+99)
Using sum of n integers formula = n * (n+1)/2) where , n=99
A100= 2+2 * [99 * (99 + 1)] / 2
A100 = 2+(99 * 100)
A100 = 9902
Answer: 9902

Is this solution Helpfull? Yes (1) | No   

Nishtha shree  (7 years ago)

A(100)=A(99)+2*99
similarly
A(99)=A(98)+2*98
A(98)=A(97)+2*(97)
:
:
:
A(2)=A(1)+2*1
so
A(100)={2*(99+98+97+......+1)+A(1)}
A(100)={2*(99+98+97+......+1)+2}
A(100)=2*99/2(99+1)+2=9902

Is this solution Helpfull? Yes (1) | No   

supriya malakar  (8 years ago)

Given A1 = 2
An+1 = An + 2n

Next number in the sequence will be,
A2 = A1 + 2*1 which can be written as,
A2 – A1 = 2*1 ------------- eqn.1
A3 – A2 = 2*2 -------------- eqn.2
A4 – A3 = 2*3 ---------------- eqn.3
and so on till,


A100 – A99 = 2*99 ------------------ eqn.99
By adding all the above eqns. we get,
A100 – A1 = 2*(1+2+3+4+……… + 99)
(using sum of n integers formula = n * (n+1)/2)
n=99
A100 – A1 = 2 * [99 * (99 + 1)] / 2
A100 – A1 = 99 * 100
A100 – A1 = 9900
A100 = 9900 + 2 = 9902

Is this solution Helpfull? Yes | No   

Rajat Agarwal  (7 years ago)

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

Is this solution Helpfull? Yes | No   

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