## plohrr 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. plohrr

@Hero @ganeshie8

2. plohrr

@SolomonZelman @jim_thompson5910

3. jim_thompson5910

5r = -10 r = ???

4. plohrr

-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. plohrr

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. plohrr

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. plohrr

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. plohrr

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. plohrr

So how do i set up the equation ? im confused

15. plohrr

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. plohrr

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. plohrr

Ok, so you leave the an as it is

21. myininaya

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

22. plohrr

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. mabitrix

the answer is A!!!!!!!!!!!!!!!!!