SOLUTION: Find the value of the following summation:<pre>{{{sum((2n-5),n=15,47)}}}{{{""=""}}}

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Question 1054498: Find the value of the following summation:
sum%28%282n-5%29%2Cn=15%2C47%29%22%22=%22%22 

Answer by Edwin McCravy(20056) About Me  (Show Source): 

You can put this solution on YOUR website!
 Find the value of the following summation:
sum%28%282n-5%29%2Cn=15%2C47%29%22%22=%22%22

We write out the first few terms, and the last term:

[2(15)-5] + [2(16)-5)] + [2(17)-5] + [2(18)-5] + ... + [2(47)-5}

[30-5] + [32-5] + [34-5] + [36-5] + ... + [94-5]

25 + 27 + 29 + 31 + ... + 89

We see this is an arithmetic series, with a1 = 25,
d = 2, and an = 89

We first use the nth term formula to find n:

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

89%22%22=%22%2225%2B%28n-1%292

89%22%22=%22%2225%2B2%28n-1%29

89%22%22=%22%2225%2B2n-2

89%22%22=%22%222n%2B23

66%22%22=%22%222n

33%22%22=%22%22n

Then we use the sum formula:

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

S%5B33%5D%22%22=%22%22expr%2833%2F2%29%2825%2B89%29

S%5B33%5D%22%22=%22%221881

Answer: 1881

Edwin