Formulas and Functions

[theachiever]

In the sequence x0,x1,x2,x3.......xn each term from x1 to xk is 3 greater than the previous term,and each term from xk+1 to xn is 3 less than the previous term,where n and k are positive integers and k<n.
If x0=xn=0 and if xk=15, what is the value of n ?

• A.5
  B.6
  C.9
  D.10
  E.15

[savvysatyam]

It will be D.

x0 is 0. now moving in the steps of 3 we will get the values as 3,6,....15. at x=5, it will be 15. now as per question k becomes 5 and from k+1th term value decreases by 3. hence 6th term onwards it will decrease finally the 10th term becomes 0.

I think this would be a fairly easy level question on GMAT

[Anurag@Gurome]

In the sequence x0,x1,x2,x3.......xn each term from x1 to xk is 3 greater than the previous term,and each term from xk+1 to xn is 3 less than the previous term,where n and k are positive integers and k<n.
If x0=xn=0 and if xk=15, what is the value of n ?

• A.5
  B.6
  C.9
  D.10
  E.15

If x0 = xn = 0 and if xk = 15, then the series will be: 0, 3, 6, 9, 12, 15,...
So, x(k + 1) = 12 implies the series is ..., 12, 9, 6, 3, 0
Hence the sequence, x0, x1, x2, x3......., xn will be: 0, 3, 6, 9, 12, 15, 12, 9, 6, 3, 0.
It can be seen that there are 11 terms in the sequence. So, x(n + 1) = 11, which implies n = 10

The correct answer is D.