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Sequence Question

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by Tdot23 » Thu May 31, 2012 8:02 am
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.
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by Anurag@Gurome » Thu May 31, 2012 8:46 am
NYC23 wrote: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
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