anilnandyala wrote:
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}?
A. 1,800
B. 1,845
C. 1,890
D. 1,968
E. 2,016
We see that the sequence is:
6, 12, 18, 24, …
This is an arithmetic sequence with first term S1 = 6 and common difference d = 6.
Recall that S_n = S1 + d(n - 1), so S13 = 6 + 6(13 - 1) = 78 and S28 = 6 + 6(28 - 1) = 168. To find the sum of a list of consecutive terms of an arithmetic sequence, we can use the formula:
(number of terms) x (first term + last term)/2
Here, the number of terms = 28 - 13 + 1 = 16, the first term = S13 = 78, and the last term = S28 = 168; thus; the sum of the terms form S13 to S28, inclusive, is:
16 x (78 + 168)/2
16 x 123
1,968
Answer: D
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