Sequence Question

[Tdot23]

Hi Everyone,
Just a quick Q from the flashcards from Manhattan GMAT.

Q: What is the 25th term of this sequence? Sn = S(n-1)subscripted - 10 and S3 = 0.
A: The guide says to first convert the recursive sequence definition provided into a direct sequence formula. Therefore Sn = -10n + k where K is the constant, then use S3 to find the value for K. I don't quite understand the direct sequence formula of Sn = -10n + k... [The guid also says to plug in 0 for S3 to get to S25 but that takes too long that is the way I first attenmpted]

If anyone could please advice I would appreicate it. Thank you.

[Anurag@Gurome]

What is the 25th term of this sequence? Sn = S(n-1)subscripted - 10 and S3 = 0.

S(n) = S(n - 1) - 10

Hence,

• S(1) = S(0) - 10
  S(2) = S(1) - 10 = S(0) - 20
  S(3) = S(2) - 10 = S(0) - 30
  S(4) = S(3) - 10 = S(0) - 40
  ...
  S(n) = S(0) - 10*n

Now, S(3) = 0 ---> S(0) = 30

Hence, S(25) = S(0) - 250 = 30 - 250 = -220