SOLUTION: express 7+13+19+...+61 using sigma notation

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Question 1081532: express 7+13+19+...+61 using sigma notation
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
This is an arithmetic sequence. Take note how we add 6 each time to generate the next term (eg: 7+6 = 13, 13+6 = 19, etc)

The common difference is therefore d = 6.

The first term is 7, so a%5B1%5D+=+7

The nth term a%5Bn%5D is

a%5Bn%5D+=+a%5B1%5D%2Bd%28n-1%29

a%5Bn%5D+=+7%2B6%28n-1%29

a%5Bn%5D+=+7%2B6n-6

a%5Bn%5D+=+6n%2B1

So the sigma notation summation would be

sum%286k%2B1%2Ck=1%2C10%29

Notice how plugging k = 1 leads to
6*k+1 = 6*1+1 = 7
which is the first term of the summation string "7+13+19+...+61"

while plugging k = 10 leads to
6*k+1 = 6*10+1 = 60+1 = 61
which is the last term of the summation string "7+13+19+...+61"

Note: solving 6k+1 = 61 leads to k = 10

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Final Answer: sum%286k%2B1%2Ck=1%2C10%29