## anonymous one year ago What is the sum of the first n terms of this series? 4 + 6 + 8 + 10 + 12 + ⋯

1. anonymous

2. alekos

its asking for the first n terms so your looking for a sum from 1 to n

3. some.random.cool.kid

...

4. SolomonZelman

The sigma notation isn't hard. You are summing from $$i=1$$ (from 4) till $$i=n$$ (some nth term which we don't know, but don't need for the sigma) Your pattern here is +2 every time, and you start from 4 Hint: (Think of a line that has a slope 2, and goes through the point (1,4) )

5. SolomonZelman

(I don't want to give it away, but do want to help.... apologize if it is not enough.

6. zzr0ck3r

$$\sum_{k=1}^n(2k+2)=2\sum_{k=1}^nk+\sum_{k=1}^n2=2\dfrac{n(n+1)}{2}+2n=n^2+3n$$ Let me know if you have any questions.