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.

• Placement Papers
• /
• TCS

TCS Question Papers: TCS Interview Experience(90) TCS Company Profile

(#M40028452) TCS question number system Keep an EYE

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 (10 years ago)

Unsolved Read Solution (3)

Is this Puzzle helpful?   (4)   (2) Submit Your Solution

Read Solution (3) :

Mohona Ghosal  (10 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

Is this solution Helpfull? Yes (39) | No   

way  (10 years ago)

9902 is the answer

Is this solution Helpfull? Yes (3) | No   

Sri Reddy  (10 years ago)

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

Is this solution Helpfull? Yes (1) | No   

Please Login to Read Solution.