SOLUTION: Can you find the sum of the first 60 terms in the series 2+6+4+12+6+24

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Question 959558: Can you find the sum of the first 60 terms in the series 2+6+4+12+6+24
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Break the 60 term series up into the sum of the 30 term 
series of odd numbered terms and the 30 term series of the
even numbered terms.  That is

2+6+4+12+6+24+... = 2+4+6+... +6+12+24+... 

The first series is arithmetic and the second one is geometric:

to find the sum of 2+4+6+... to 30 terms we use the formula:

S%5Bn%5D%22%22=%22%22expr%28n%2F2%29%282a%5E%22%22%2B%28n-1%29d%29, where a%5B1%5D=2, n=30, and d=2

S%5B30%5D%22%22=%22%22expr%2830%2F2%29%282%282%29%5E%22%22%2B%2830-1%292%29 

S%5B30%5D%22%22=%22%2215%284%5E%22%22%2B%2829%292%29

S%5B30%5D%22%22=%22%2215%284%2B58%29

S%5B30%5D%22%22=%22%2215%2862%29

S%5B30%5D%22%22=%22%22930

---

To find the sum of 6+12+24+... to 30 terms we use the formula:

S%5Bn%5D%22%22=%22%22%28a%5B1%5D%28r%5En-1%29%29%2F%28r-1%29, where a%5B1%5D=6, n=30, and r=2

S%5B30%5D%22%22=%22%226%282%5E30-1%29%2F%282-1%29

S%5B30%5D%22%22=%22%226%281073741824-1%29%2F%281%29

S%5B30%5D%22%22=%22%226%281073741823%29

S%5B30%5D%22%22=%22%226442450938

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The sum of the two sequences is  930+6442450938 = 6442451868

Edwin