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infinite sequence

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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by swapna » Fri Apr 09, 2010 11:33 am
If S is the infinite sequence S1 = 6, S2 = 12, ..., Sn = Sn-1 + 6,..., what is the sum of all terms in the set {S13, S14, ..., S28}?

1,800
1,845
1,890
1,968
2,016

ans d

I remember vaguely that there was a formula for such problems.can some one help me??
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by papgust » Fri Apr 09, 2010 6:49 pm
First find what S13 is.

Sn = a+(n-1)d

a = first term (S1), d = common difference (6)

S13 = 6+(12)6
S13 = 78

Now find out what S28 is.

S28 = 6+(27)6
S28 = 168

You now know S13 and S28. Now you need to calculate sum of all terms ranging from S13 to S28 inclusive.

Sum = n/2 [first term + last term]

n = number of terms [(28-13)+1 = 16]
first term = S13
last term = S28

Sum = 16/2 [S13+S28] = 16/2 [78+168] = 8 * 246 = 1,968
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by swapna » Sat Apr 10, 2010 12:40 pm
thanks....u helped me recollect the formula:-)
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by liferocks » Sat Apr 10, 2010 7:14 pm
just wanted to post one small tip,
here we don't actually have to calculate 8 * 246 = 1,968
because 8*6 is 48 ,hence the last digit of ans will be 8..only one of the options has that.
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