## anonymous one year ago What are the explicit equation and domain for a geometric sequence with the first term of 5 and a second term of -10?

1. anonymous

an=5(-2)^(n-1); all integers when n≥1 an=5(-2)^(n-1); all integers where n≥0 an=5(-15)^(n-1); all integers where n≥1 an=5(-15)^(n-1); all integers where n≥0

2. anonymous

@ganeshie8

3. anonymous

@phi

4. anonymous

@dan815

5. anonymous

yay @phi is here

6. anonymous

I'm pretty sure the second half is n≥1

7. anonymous

right?

8. phi

You could test each choice. You should get 5, -10 as the first two numbers.

9. anonymous

a

10. anonymous

wait

11. anonymous

b

12. anonymous

no a

13. anonymous

omg im so confused

14. phi

***an=5(-2)^(n-1); all integers when n≥1*** for n=1 you get $a_1 = 5(-2)^{1-1} \\ a_1 = 5\cdot (-2)^0$ anything to the zero power is 1 , so that simplifies to $a_1= 5 \cdot 1 \\a_1=5$ that looks good so far

15. phi

now find a2 for choice A, using n=2

16. anonymous

a2=5(-2)^(2-1) =5(-2)^1 =-10

17. phi

yes. so choice A looks like the answer. You could double check the other three, but they won't work (give 5, -10)

18. anonymous

ok thank you i have another but i don't know how to post the graphs so oh well

19. phi

do you know how to take a screen shot?

20. anonymous

the wording is horrible

21. anonymous

yeah put its on my other computer hang on

22. anonymous

It says which logarithmic graph can be used to approximate the value of y in the equation 2^y=3

23. anonymous

i don't know how to log that?

24. phi

take the log of both sides. Log base 2 is the most convenient, but log base 10 or log base 3 (natural log) all can be used. use the "rule" $\log(a^b) = b \log(a)$

25. anonymous

so… log10 2^y= log10 3

26. phi

and then use the rule to write $y \log 2 = \log 3 \\ y = \frac{\log 3}{\log 2}$

27. phi

to get the answer from a graph, we need to figure out what log base they used. for example, what is the x value that corresponds to y=1 (that should give us the base)

28. phi

Here are 3 possible logs if they gave you log base 2, read off the y value at x=3

29. anonymous

thank you i got it