SOLUTION: Write the series with summation notation: 2+5+8+11+...

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Question 959118: Write the series with summation notation: 2+5+8+11+...
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Write the series with summation notation: 2+5+8+11+...
2
2+1*3 = 5
2+2*3 = 8
2+3*3 = 11
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a(n) = 2 + 3n
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Answer: S(n) = Summation (as n goes from 0 to k) of (2+3n)
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Cheers,
Stan H.
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Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Method #1

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Method #2

Notice how we add 3 to each term to get the next term (2+3 = 5, 5+3 = 8, etc). This points to the fact that we have an arithmetic sequence.

So the common difference is d = 3

The first term is a(1) = 2

Use these two facts to get the nth term

a(n) = a(1) + d(n-1)
a(n) = 2 + 3(n-1)
a(n) = 2 + 3n-3
a(n) = 3n - 1

So because the nth term is 3n-1 this means that $2+5+8+11+... = \sum_{k=1}^{\infty}(3k-1)$ (the only difference is that I'm using k instead of n as the index)

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