Question

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

Answer 1

In one site i got solution...
but i did not understant.....

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

Answer 2

plz any one understand explain me...

Answer 3

a[1] = 0;
a[2] = 2 (1)
a[3] = 2 (1) + 2 (2)
a[4] = 2 (1) + 2 (2) + 2 (3)

a[n + 1] = 2 ( 1 + 2 + n) = n (n + 1)

a[100] = 99 x100=9900

Answer 4

No the answer is 9902...

Answer 5

Is a(1)=0

Answer 6

ya...

Answer 7

So what is wrong with my computation above?

Answer 8

In my book given answer is 9902...

Answer 9

they have given the solution....
but i did not understand it....

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

Answer 10

Either the problem is not stated right or the answer in your book is wrong

Answer 11

kk thankyou....:-)

Answer 12

Do you know the the formula
\[
1+1 +3 + \cdots + n= \frac{n(n+1)}2
\]

Answer 13

ya i know....

Answer 14

\[
1+2 +3 + \cdots + n= \frac{n(n+1)}2
\]

Answer 15

ya...

Answer 16

That is all what you need to do your problem

Answer 17

kk... i think my solution is wrong....

thanx for your help...