## anonymous one year ago Does anyone know how to do this Sigma Notation question?

1. anonymous

This

2. SolomonZelman

ok. your common ratio (r) is? your first term ($$a_1$$) is? your number of terms (n) is?

3. anonymous

I have absolutely no clue how to figure out those thing my teacher never taught me

4. anonymous

@SolomonZelman

5. SolomonZelman

6. anonymous

No :(

7. SolomonZelman

what is this: $$\large\color{black}{ \displaystyle 2(-2)^{n-1} }$$ when n=1?

8. anonymous

-2?

9. SolomonZelman

$$\large\color{black}{ \displaystyle 2(-2)^{n-1} }$$ when n=1: $$\large\color{black}{ \displaystyle2(-2)^{1-1} =2(-2)^0=2\cdot 1=2}$$

10. SolomonZelman

Ok, can you tell me what is $$\large\color{black}{ \displaystyle 2(-2)^{n-1} }$$ when n=2?

11. SolomonZelman

plug in 2 instead of n....

12. anonymous

-4?

13. anonymous

@SolomonZelman

14. SolomonZelman

yes

15. SolomonZelman

ok, now do the same when n=3

16. anonymous

8

17. SolomonZelman

yes.

18. SolomonZelman

So so frar your terms are: 2, -4, 8.... do you notice any pattern?

19. SolomonZelman

you multiply times -2 every time, is this correct?

20. anonymous

yes'

21. SolomonZelman

Ok, and this number by which you multiply every time (if a sequence is like yours, that follows a multiplication pattern), is called "common ratio" and is denoted by letter r.

22. SolomonZelman

So, we can say that r=-2

23. SolomonZelman

Now, what does your sequence start from, what is the first term?

24. anonymous

2

25. SolomonZelman

yes

26. SolomonZelman

so we can say that the first term is 2. $$a_1=2$$ ----------------------------- (NOTATIONS) A first term is denoted by $$a_1$$ Second term is denoted by $$a_2$$ Third term is denoted by $$a_3$$ any nth term is denoted by $$a_n$$ -----------------------------

27. SolomonZelman

And then your number of terms is 7 (i colored it in blue) $$\Large\color{black}{ \displaystyle \sum_{ n=1 }^{\color{blue}{7}} 2(-2)^{n-1} }$$

28. SolomonZelman

so, now, again, pliz answer my 3 questions that I asked in the very beginning.

29. anonymous

your common ratio (r) is? -2 your first term (a1) is? 2 your number of terms (n) is? 7

30. anonymous

@SolomonZelman

31. freckles

do you still need help on this ?

32. freckles

you can use the formula $a_1 \cdot \frac{1-r^{n}}{1-r}$ and enter in all that info you and @solomonzelman found together

33. SolomonZelman

My power went off for a couple of hours due to a rail. I don't even think that "rail" is a good name for what happened... in any case; my apologies, and good luck!

34. SolomonZelman

and the answers to my initial 3 questions are correct, good job.