SOLUTION: solve- 1+6+11+16+....+x=148

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Question 877961: solve-
1+6+11+16+....+x=148
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Formula for Arithmetic Series, S=%28n%2F2%29%28a%5B1%5D%2Ba%5Bn%5D%29 or S=%28n%2F2%29%282a%5B1%5D%2B%28n-1%29d%29 in which d is the common difference between sequence terms.

Your equation does not indicate the actual last term or its index. The formula using the common difference should be a good choice.

Your equation shows d=5 and a%5B1%5D=1.
%28n%2F2%29%282%2A1%2B%28n-1%29%2A5%29=148, applying that second version of the formula.
%28n%2F2%29%282%2B5n-5%29=148
n%28-3%2B5n%29=296
5n%5E2-3n=296
highlight_green%285n%5E2-3n-296=0%29.
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Discriminant: 9+4*5*296=5929, and sqrt(5929)=77.
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GENERAL SOLUTION FOR QUADRATIC EQUATION GIVES THIS RESULT...
n=%283%2B-+77%29%2F%282%2A5%29, the PLUS-form makes sense.
n=%283%2B77%29%2F10
n=80%2F10
highlight%28n=8%29
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So what is x ?
x is the eighth term of the sequence.
General term of the sequence: 1%2B%28n-1%29%2A5;
using n=8, x=1%2B%288-1%29%2A5,
x=1%2B7%2A5
highlight%28highlight%28x=36%29%29.
You can fill-in the other terms if you want.


1+6+11+16+21+26+31+36=148