## Tabbiejack 2 years ago Write the explicit formula for the geometric sequence. a1 = -5 a2 = 20 a3 = -80 A. an = -5 • (-4)n B. an = -5(-4)n-1 C. an = -4(-5)n-1 D. an = -5 • (4)n

1. bahrom7893

look a1 = -5 n=1 a2=20 n=2, etc..

2. Jhannybean

It would be B because in a geometric sequence, you have $\large ar ^{n-1}$ and in finding our r, we take $$\large\frac{ a _{2} }{ a _{1} }$$ and that is -4

3. bahrom7893

This way you can eliminate A because term 2 doesn't match up... And I think Jhanny's right

4. Tabbiejack

thanks you that was heard

5. Jhannybean

So we have a1 = -5, our r = -4 and plug it into our formula $\large ar ^{n-1}$

6. Jhannybean

thanks bahrom :)

7. Tabbiejack

Can you help me with another

8. Jhannybean

sure

9. Tabbiejack

What is the simplified form of the expression?|dw:1369539526178:dw|

10. Jhannybean

Alright, for this one you have a variable with two different powers dividing eachother, and in this case, we can simply do this. $\large \frac{ 1 }{ q ^{\color{red}{(33/4)-8} }}$

11. Jhannybean

we you know to solve $\color{fuchsia}{\frac{ 33 }{ 4 }}-\color{green}{8}$

12. Tabbiejack

|dw:1369539985575:dw|

13. Tabbiejack

That is the choices

14. Jhannybean

hmm...something seems wrong here.

15. Jhannybean

$\frac{ 33 }{ 4 }-8*(\frac{ \color{green}{4} }{ \color{green}{4} })= \frac{ 33 }{ 4 }-\frac{ \color{darkorchid}{32} }{ \color{darkorchid}{4} }$

16. Jhannybean

Ohh I see. hm, well what do you get when you reduce 33/4- 32/4? :D

17. Tabbiejack

I am confused

18. Jhannybean

hm?

19. Tabbiejack

I have no Idea what the answer is

20. Jhannybean

solve (33/4)-(32/4) and we'll work from there, you'; get your answer, promise :)

21. Tabbiejack

I am the parent of 2 children that is failing

22. Tabbiejack

this looks like greek to me..

23. Jhannybean

ok, what is.... 3-2?

24. Tabbiejack

1

25. Jhannybean

good :) so 33-32 works the same way, it is also 1.

26. Jhannybean

So we now have $\frac{ 1 }{ q ^{\color{blue}{1/4}} }$

27. Tabbiejack

o ok

28. Tabbiejack

I thank you so much

29. Tabbiejack

algebra has always been my worst subject

30. Jhannybean

It'll get better with practice :) Practice makes people perfect in math ^_^

31. Tabbiejack

I remember hearing that when I was young

32. Tabbiejack

I have another quesiton if you are up to it?

33. Jhannybean

Of course :) Math is a lot about understanding a problem as a whole and finding a relation to a technique method in solving, it's all patterns.

34. Jhannybean

sure thing

35. Tabbiejack

I have 2 test to give to my children for the summer to help them prepare for summer school that is why I am getting the answers so I will be able to help them

36. Jhannybean

Interesting

37. Tabbiejack

What is the simplified form of the expression?|dw:1369541274406:dw|

38. Jhannybean

$\large (3x ^{\color{forestgreen}{7/2}})^{\color{blue}{6}}(x ^{\color{green}{2}})^{\color{blue}{6}}$ here, we will start 1 part at a time. lets start with $$\large (3x ^{7/2})^{6}$$

39. Tabbiejack

ok what do we do next

40. Jhannybean

we're going to multiply 6 to the 3 AND the x^(7/2)

41. Jhannybean

Are you able to do that?

42. Tabbiejack

18 x

43. Tabbiejack

I suck

44. Jhannybean

Hm.. not exactly, we have $\large(3^{\color{blue}{6}})(x ^{\color{blue}{(7/2)(6)}})$ which gives us $\large(729x ^{21})$

45. Tabbiejack

A. 729x33 B. 3x33 C. 729x29 D. 3x29

46. Jhannybean

Now that we've taken care of the first part, we can move onto the second part, which is $\large (x ^{2})^{6} = x ^{\color{red}{6*2}}= x ^{\color{blue}{12}}$

47. Tabbiejack

ok

48. Jhannybean

Now we can combine both parts together so we get $\large (729x {^\color{green}{21}}) *(x ^{\color{green}{12}}) = 729x ^{\color{red}{21+12}}$

49. Jhannybean

50. Jhannybean

Good luck with your other problems!

51. Tabbiejack

33

52. Tabbiejack

729x^33

53. Tabbiejack

am I right?

54. Tabbiejack

thanks so much