SOLUTION: sum of first 20 terms of an arithmetic sequence is 900. sixth term is 27. what is its fifteenth term and common difference.

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Question 755524: sum of first 20 terms of an arithmetic sequence is 900. sixth term is 27. what is
its fifteenth term and common difference.
Answer by reviewermath(1029) About Me  (Show Source):
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Q:
sum of first 20 terms of an arithmetic sequence is 900. sixth term is 27. what is
its fifteenth term and common difference.
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A:
In arithmetic sequence, the sum of the first n terms is equal to
S%5Bn%5D = %28n%2F2%29%28a%5B1%5D+%2B+a%5Bn%5D%29
The sixth term is a%5B6%5D = 27, if the common difference is d then the first term is a%5B1%5D = 27 - 5d and the 20th term is a%5B20%5D = 27 + 14d.
S%5B20%5D = %2820%2F2%29%28a%5B1%5D+%2B+a%5B20%5D%29
900 = %2820%2F2%29%28%2827+-+5d%29+%2B+%2827+%2B+14d%29%29
900 = 10%289d+%2B+54%29
9d + 54 = 90
d = 4
a%5B1%5D = 27 - 5(4) = 7
The nth term is a%5Bn%5D = 7 + 4(n - 1) = 4n + 3
The 15th term is a%5B15%5D = 4(15) + 3 = 63
Here are the answers:
15th term: highlight%2863%29 and common difference, d = highlight%284%29