SOLUTION: Find the indicated sum: 6 + 12 + 18 + ... + 300

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Question 968156: Find the indicated sum:
6 + 12 + 18 + ... + 300

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Find the indicated sum:
6 + 12 + 18 + ... + 300
One of two formula for the sum of n terms is

S%5Bn%5D%22%22=%22%22expr%28n%2F2%29%28a%5B1%5D%2Ba%5Bn%5D%29

We have a1 = 6 and an = 300

so we must find d and n

6 + 12 + 18 + ... + 300

First we determine the common difference, d

d = (2nd term)-(1st term) = (3rd term)-(2nd term) = 12-6 = 18-12 = 6

Next we determine the number of terms, n:

We use the formula for the nth term

a%5Bn%5D%22%22=%22%22a%5B1%5D%2B%28n-1%29d

300%22%22=%22%226%2B%28n-1%296

300%22%22=%22%226%2B6%28n-1%29

300%22%22=%22%226%2B6n-6

300%22%22=%22%226n

50%22%22=%22%22n

Now we can substitute in

S%5Bn%5D%22%22=%22%22expr%28n%2F2%29%28a%5B1%5D%2Ba%5Bn%5D%29

S%5B50%5D%22%22=%22%22expr%2850%2F2%29%286%2B300%29

S%5B50%5D%22%22=%22%2225%28306%29

S%5B50%5D%22%22=%22%227650

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Notice that we could have used the other sum formula just as well:

S%5Bn%5D%22%22=%22%22expr%28n%2F2%29%282%5E%22%22a%5B1%5D%2B%28n-1%29d%29

S%5B50%5D%22%22=%22%22expr%2850%2F2%29%282%286%29%5E%22%22%2B%2850-1%296%29

S%5B50%5D%22%22=%22%2225%2812%5E%22%22%2B%2849%296%29

S%5B50%5D%22%22=%22%2225%2812%2B294%29

S%5B50%5D%22%22=%22%2225%28306%29

S%5B50%5D%22%22=%22%227650

Edwin