# Thread: Find the sum of the given arithmetic series

1. ## Find the sum of the given arithmetic series

Find the sum of the given arithmetic series. Do not just add, you must use the formula
$\displaystyle \sum_{i=1}^6\left( \frac{-5}{2}i+3\right)$

What formula is used and how do I start this. I never seen this type of example as I only seen whole numbers used.

2. Originally Posted by ToXic01
Find the sum of the given arithmetic series. Do not just add, you must use the formula
$\displaystyle 6 Sigma ((-5/2)+3) i=1$

What formula is used and how do I start this. I never seen this type of example as I only seen whole numbers used.
Is this your equation $\displaystyle \sum_{i=1}^6\left( \frac{-5}{2}+3\right)i = 1$ ??

3. I fixed the problem

4. Go from $\displaystyle 1$ to $\displaystyle 6$

$\displaystyle \left( \frac{-5}{2}{\color{red}\times 1}+3\right)+\left( \frac{-5}{2}{\color{red}\times 2}+3\right)+\dots+\left( \frac{-5}{2}{\color{red}\times 6}+3\right)$

You got it?

5. Yeah i know that process but I am not allowed to just add. The question wants me to use the formula. Thanks

6. it is a very easy and simple issue
you just have to use the formula : the sum=number of terms over 2 times ("open brackets first term+last term)
here it is 6/2[1/2+(-12)]=-69/2
you are most welcomed
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