Saiyan one year ago Help I don' t understand how to do this question! I will give medals

1. Saiyan

2. Saiyan

I think it is b

3. IrishBoy123

$$S = 4 + 3 + 2 + .... + \ (-14) + \ (-15)$$ but reverse it and: $$S = (-15) + (-14) + ... + \ 3 + \ 4$$ so $$2S = S + S = \ ...???$$

4. IrishBoy123

-15 + 4 = -11 -14 + 3 = -11 etc etc

5. Saiyan

yeah i tried that and i got -130

6. Saiyan

4+3+2+1+0-1-2-3-4-5-6-7-8-9-10-11-12-13-14-15-16

7. jdoe0001

@Saiyan what would be the 1st term in the sequence?

8. Saiyan

what do u mean

9. IrishBoy123

-130 !!! you have 20 terms in the sequence, right?!?! as you're summing from n = 1 to 20

10. IrishBoy123

continue with this and you will get there

11. jdoe0001

well, is a sequence , notice $$\large \bf \sum\limits_{n=1}^{20}\quad (5-n)\qquad thus\qquad a_1=?$$

12. jdoe0001

$$\large a_1=first\ term=?$$

13. jdoe0001

$$\large \begin{array}{llll} \sum\limits_{{\color{brown}{ n=1}}}^{20}\\ \ \uparrow \\ hint \end{array}$$

14. IrishBoy123

so that's 20 x (-11) / 2 yes?

15. Saiyan

yeah

16. jdoe0001

ahemmm using $$\large S_n=\cfrac{n}{2}(a_1+a_n)$$ yes