Question 691886: The answer to the question is 15 terms. But, I can't find the answer without knowing what to find, first. I tried the formulas and to no avail. Here is the question, "How many terms are in the sum of an arithmetic sequence if the first term is 21, the common difference is 9 and the sum is 1,260?"
I know that (a one) is 21, d=9 and n=1260
I first tried to see if 1,260 could be a term and calculated it with the An = A1 + (n-d)d and that didn't work. Then, I tried to plug in the numbers with the Sn=n(A1+An)/2, that further confused me. I have no idea what to do when provided the total first and how to work from that in order to find the terms. There are no examples in both my math books and I'm stuck. Help.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! "How many terms are in the sum of an arithmetic sequence if the first term is 21, the common difference is 9 and the sum is 1,260?"
I know that (a one) is 21, d=9 and n=1260
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Sum Formula:
S(n) = (n/2)(a(1)+(a(n)))
1260 = (n/2)(21 + [21+ (n-1)9]
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1260 = (n/2)[42+9n-9]
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2520 = (n)[33+9n]
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2520 = 33n + 9n^2
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3n^2 + 11n - 840 = 0
(n-15)(3n+ 56) = 0
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Positive solution:
n = 15
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cheers,
Stan H.
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