# Thread: arithmetic series or sequences...

1. ## arithmetic series or sequences...

i need help with two questions...

1. find the suma of all the intergers between 1 and 200 that are not multiples of 7.

and i have just realised that i have no idea how to do sigma questions on herebut i'll try to describe it.

2. find (at the bottom of the sigma sign r=1 and at the top of it n then next to it 1-(r/3)), giving your answer in the form (n/a)(b-n), where a and b and intergers.

thanks for any help

thanks again

2. #1: The sum of the first 200 integers excluding the multiples of 7 (i.e. from 7, 14, 21, ..., to 196) is equal to the total sum of the first 200 integers minus the sum of the multiples of 7:
$\displaystyle \underbrace{\sum_{n=1}^{200} n}_{\text{Sum of 1 to 200}} \ - \ \underbrace{\sum_{n=1}^{28} 7n}_{\text{Sum of 7 + 14 + 21 + ... + 196}}$

$\displaystyle \sum_{r = 1}^{n} \left(1 - \frac{r}{3}\right)\ \ = \ \ \sum_{r=1}^{n} 1 - \sum_{r=1}^{n} \frac{r}{3}\ \ = \ \ \sum_{r=1}^{n} 1 - \frac{1}{3}\sum_{r=1}^{n} r \ \ = \ \ \hdots$

3. ok i get #1 but i'm still not with #2 could you please explain ti a bit more

thanks

4. What don't you understand?

You should know these: $\displaystyle \sum_{i=1}^{n}1 = \underbrace{1 + 1 + \hdots + 1}_{n \text{ times}} = n$.......$\displaystyle \sum_{i=1}^{n} i = 1 + 2 + 3 + \hdots + n = \frac{n(n+1)}{2}$

Just a matter of simplifying after you substitute those in.

5. ok i get it now must have read it wrong before thanks for explaining ti again though