SOLUTION: I really need help with this question. Find the sum of 34+35+36+37+...+102+103 I have been trying to figure it out, but now I am just getting frustrated. Please help me step by

Algebra ->  Expressions -> SOLUTION: I really need help with this question. Find the sum of 34+35+36+37+...+102+103 I have been trying to figure it out, but now I am just getting frustrated. Please help me step by       Log On


   

Question 986399: I really need help with this question.
Find the sum of 34+35+36+37+...+102+103
I have been trying to figure it out, but now I am just getting frustrated. Please help me step by step on what I am actually supposed to do!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
This is an arithmetic sequence with common difference of d = 1. The first term is a = 34

Subtract the last term and first term to get: 103-34 = 69. Add on 1 to get 69+1 = 70. So there are 70 terms in the summation above. This means n = 70

We have these three values
a = 34
d = 1
n = 70

Plug them into the arithmetic sum formula. Doing all that will give you

S%5Bn%5D+=+%28n%2A%282%2Aa%2Bd%2A%28n-1%29%29%29%2F2

S%5B70%5D+=+%2870%2A%282%2A34%2B1%2A%2870-1%29%29%29%2F2

S%5B70%5D+=+4795

In the end, 34+35+36+37+...+102+103 = 4,795


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If you need more help, or if you have any questions about the problem, feel free to email me at jim_thompson5910@hotmail.com