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

1. anonymous

@Hero @ganeshie8

2. anonymous

@SolomonZelman @jim_thompson5910

3. jim_thompson5910

5r = -10 r = ???

4. anonymous

-2

5. jim_thompson5910

First Term: a = 5 Common Ratio: r = -2 Plug those into $\Large a_{n} = a*(r)^{n-1}$ to get the general nth term formula

6. anonymous

5n = 5 x (-2) n-1 5n = -10 n-1 What do i do from here

7. myininaya

no a_n symbolizes the n term of the sequence a_n and a are different values also we don't have (ar)^(n-1) we just have that the r is to the (n-1)

8. anonymous

Ok, so how do i set up this equation

9. myininaya

$a_n=a \cdot r^{n-1}$ just replace the a with 5 and replace the r with -2 like jim said

10. anonymous

5n = -10^n-1 ?

11. myininaya

again a_n and a are different values a_n is a variable by itself you can't multiply a and r because r has an exponent

12. anonymous

5_n = 5 x -2^n-1

13. myininaya

you cannot replace a_n with 5_n this makes no sense let me show you how this formula is come up with so maybe you understand better {a_n} is a sequence of numbers those numbers are a_1=5 a_2=5(-2)=-10 a_3=5(-2)(-2)=5(-2)^2=20 a_4=5(-2)(-2)(-2)=5(-2)^3=-40 a_5=5(-2)(-2)(-2)(-2)=5(-2)^4=80 ... therefore a_n=5(-2)(-2)(-2)(-2)(-2)(-2)...(-2)= (by the way that is a (n-1) amount of (-2)) I put a (n-1) amount of (-2) because looking at a_1 we have (-2)^0=(-2)^(1-1) looking at a_2 we have (-2)^1=(-2)^(2-1) looking at a_3 we have (-2)^2=(-2)^(3-1) it is always one less than where the number is in the sequence

14. anonymous

So how do i set up the equation ? im confused

15. anonymous

Does the 5 not go where the n is

16. jim_thompson5910

5 goes where 'a' is but $$\Large a_n$$ is NOT the same as just 'a'

17. jim_thompson5910

If it confuses you, think of it as $\Large T = a*(r)^{n-1}$ T = nth term a = first term r = common ratio n = positive whole number (used to identify which term you're dealing with) example: n = 3 ---> 3rd term

18. anonymous

Ok

19. jim_thompson5910

The notation $$\Large a_n$$ is used for sequences because the 'n' changes to a positive whole number to indicate a certain term example: 17th term ---> n = 17 ---> $$\Large a_n = a_{17}$$

20. anonymous

Ok, so you leave the an as it is

21. myininaya

Yep it is a formula for the nth term in the sequence

22. anonymous

So it is an = 5 (-15)^n-1; all integers where n less than or equal to 1

23. myininaya

how do you get -15 for r?

24. myininaya

r symbolizes the geometric ratio to find r all you have to do is evaluate a_2/a_1 or take any two consecutive numbers in the sequence and put the 2 nd term of those numbers over the 1st term of those numbers

25. myininaya

also this was already determined way above when joe was working with you

26. anonymous