## anonymous one year ago Write the sum using summation notation, assuming the suggested pattern continues. -8 - 3 + 2 + 7 + ... + 67

1. anonymous

@IrishBoy123

2. IrishBoy123

this one is arithmetic, right? so what is the common difference?

3. anonymous

5

4. IrishBoy123

yes so $$a_1 = -8$$ $$a_2 = -8 + 1(5)$$ $$a_3 = -8 + 2(5)$$ we will want a general term for $$a_n$$, the nth term in this sequence

5. IrishBoy123

can you have a go at that?

6. IrishBoy123

|dw:1438707453164:dw|

7. anonymous

Would it be:$\sum_{n=0}^{\infty}(-8+5n)$

8. anonymous

@IrishBoy123

9. IrishBoy123

if we are starting at n = 1, you need a small tweak

10. IrishBoy123

if term 1 is $$a_1$$, with $$n = 1$$

11. anonymous

sum_{n=0}^{15}(-8+5n) ?

12. anonymous

$\sum_{n=0}^{15}(-8+5n)$

13. IrishBoy123

$$a_1=−8 = -8 +5(1-1)$$ $$a_2=−8+(5)(2-1)$$ $$a_3=−8+(5)(3-1)$$

14. IrishBoy123

$$a_n = ??$$

15. anonymous

-8+5n

16. IrishBoy123

-8+5(n - ??)

17. anonymous

That's not an answer choice though. These are my answer choices: A. $\sum_{n=0}^{15}(-8+5n)$ B. $\sum_{n=0}^{\infty}(-40n)$ C.$\sum_{n-0}^{15}(-40n)$ D. $\sum_{n=0}^{\infty}(-8+5n)$

18. IrishBoy123

OK, they're doing it that way, with the first term as $$a_0$$ not $$a_1$$ in which case you go with your suggestion, $$-8+5n$$ and checking the value of $$n$$ for the last term: $$-8+5n = 67 \implies n = 15$$

19. anonymous

Ok thanks! So it would be A?

20. IrishBoy123

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