Latest TCS Aptitude Question SOLUTION: a sequence {An}is defined A(1)=0&A(n+1)=A(n)+2(n)WHAT IS VALUE OF A(100)(a)9902(B)9900(C)10100(D)9904

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a sequence {An}is defined A(1)=0&A(n+1)=A(n)+2(n)WHAT IS VALUE OF A(100)(a)9902(B)9900(C)10100(D)9904

Asked In TCS jasveer (12 years ago)

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Akanksha Narula  (12 years ago)

A(100)= A(99)+2(99)
A(100)= A(98)+ 2(98)+2(99)
A(100)= A(97)+2(97)+2(98)+2(99)
||LY
A(100)= A(1)+ 2(1+2+3+4+.......97+98+99)

NOW; 1+2+3.......+97+98+99= 99(2+98)/2= 4950
(SUM OF AN A.P)

A(100)= 0+ 2(4950)= 9900

Is this solution Helpfull? Yes (22) | No (5)  

Tanaya Konar  (12 years ago)

The answer is a.9902.first the data is incorrect in question.A(1)=2 will be the correct data.
Now
A(100)=we can write A(99+1) as A(n+1) is given so i broke it in n+1 form.
then A(99+1)=A(99)+2*99;
in this way A(99)=A(98)+2*99*98
in this way..
..
last will be A(1)+2*99*98*.....1
now put the value 1+2(1+2+......+99)
2+ 2*99(99+1)/2
=9902

Is this solution Helpfull? Yes (11) | No (15)  

SHANU MAHAJAN  (12 years ago)

hey tanaya: The que. is correct.. ans would be 9900 if A(1) is 0 as mentioned in the question.

Is this solution Helpfull? Yes (7) | No (3)  

Nabeel Ansari  (12 years ago)

ans is 9900.

Is this solution Helpfull? Yes (3) | No (1)  

jasveer   (12 years ago)

tanaya i get it half ,i don't no how u write 1+2(1+2+............+99)

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

lala  (12 years ago)

@tanaya konar
last will be A(1)+2*99*98*.....1
now put the value 1+2(1+2+......+99)
2+ 2*99(99+1)/2
=9902
can u explain these steps more clearly plz

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