SOLUTION: Given the sequence: 5,14,23,32,..., determine the 56th term and the sum of the first 57 terms.

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Question 1101404: Given the sequence: 5,14,23,32,..., determine the 56th term and the sum of the first 57 terms.
Answer by htmentor(1343) About Me  (Show Source):
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This is an arithmetic sequence with common difference = 9 and 1st term = 5
The nth term is a_n = a1 + (n-1)*d
Thus a_n = 5 + 9(n-1) = 9n - 4
Therefore a_56 = 9*56 - 4 = 500
The sum of the 1st n terms is given by S(n) = (n/2)(a1 + an)
a_57 = 9 + a_56 = 509
S(57) = (57/2)(5 + 509) = 14649