SOLUTION: Find the sum of the first twenty terms of the sequence 3,5,7,........

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Question 371414: Find the sum of the first twenty terms of the sequence 3,5,7,........
Found 2 solutions by ewatrrr, jrfrunner:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!

Hi,
sum of the first twenty terms of the sequence 3,5,7,........
sum%28%2820%2F2%29%282%2A3+%2B+19%2A2%29%2C+n=1%2C+20+%29 = 10(6+38) = 440

Answer by jrfrunner(365) About Me  (Show Source):
You can put this solution on YOUR website!
In the sequence you provide each number changes by an "constant" value.
This is known as an arithmetic sequence
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The change, or delta is the difference between any two values, so in this case delta=2
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For an arithmetic sequence, the nth term a%5Bn%5D=a%5B1%5D%2B%28n-1%29%2Adelta
and for an arithmetic series, its sum is defined as the average value times the number of terms or Sum=%28%28a%5B1%5D%2Ba%5Bn%5D%29%2F2%29%2An
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in the sequence you provide, a%5B1%5D=3 and the last term a%5Bn%5D=3%2B%2820-1%29%2A2=41
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The sum = average value * n = %28%28first+%2B+last%29%2F2%29+%2An+=%28%283%2B41%29%2F2%29%2A20=440