SOLUTION: What is the sum of the arithmetic sequence 5, 11, 17 …, if there are 24 terms?

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Question 462230: What is the sum of the arithmetic sequence 5, 11, 17 …, if there are 24 terms?
Answer by math-vortex(648) About Me  (Show Source):
You can put this solution on YOUR website!
What is the sum of the arithmetic sequence 5, 11, 17 …, if there are 24 terms?
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To find any TERM in an arithmetic sequence, we use this formula:
a%5Bn%5D=a%5B1%5D%2B%28n-1%29d
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To find the SUM of the series we'll use
S%5Bn%5D=%28n%28a%5B1%5D%2Ba%5Bn%5D%29%29%2F2
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d = the common difference between each term in the series = 6
a[1] = the first term = 5
n = the number of terms we're interested in = 24
a[n] = the nth term; in this case, the 24th term
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First, we find the 24th term,
a%5Bn%5D=a%5B1%5D%2B%28n-1%29d
a%5B24%5D=5%2B%2824-1%29%286%29
a%5B24%5D=143
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To find the sum of the series we'll use,
S%5Bn%5D=%28n%28a%5B1%5D%2Ba%5Bn%5D%29%29%2F2
S%5B24%5D=%28%2824%29%285%2B143%29%29%2F2
S%5B24%5D=1776
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hope this helps!
Ms.Figgy
math.in.the.vortex