SOLUTION: What is the sum of the arithmetic series below? 2+5+8+......+59

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Question 918715: What is the sum of the arithmetic series below? 2+5+8+......+59
Found 2 solutions by ewatrrr, rothauserc:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
d = 3
a%5Bn%5D+=+a%5B1%5D+%2B+%28n-1%29d
a%5Bn%5D+=+2+%2B+%28n-1%293
a%5Bn%5D+=3n-1
a%5Bn%5D+=3n-1+=+59, n = 20
S%5Bn%5D=%28n%28a%5B1%5D%2Ba%5Bn%5D%29%29%2F2
S%5B20%5D=20%2861%29%2F2 = 610

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
sum(S) = (n/2)*(a1 + an), where a1 is the first term and an is the nth term
we need to find n for 59
59 = a1 + (n-1)*d where d is the difference between terms
59 = 2 + (n-1)*3
57 = 3n -3
3n = 60
n = 20
returning to our sum formula
S = (20/2)*(2 + 59)
S = 10*61 = 610
our sum is 610