## egbeach one year ago Find an equation for the nth term of the arithmetic sequence. -3, -5, -7, -9, ...

1. freckles

arithemtic sequences are well known for their common difference

2. freckles

so first step: find common difference

3. Haseeb96

@freckles are you help her or should i help her?

4. freckles

it doesn't matter

5. freckles

go for it

6. Haseeb96

okay you carry on

7. Haseeb96

i am busy some other areas

8. freckles

ok -3, -5, -7, -9, ... common difference can be found be taking a term and subtracting its previous term

9. egbeach

-2

10. freckles

what is -5-(-3)?

11. freckles

yes that is right

12. freckles

$a_n=a+d(n-1) \\ \text{ so } d=-2 \\ a_n=a-2(n-1)$ a is suppose to represent the first term

13. freckles

14. egbeach

-3

15. freckles

so replacing a with -3 don't replace a_n with anything a_n thing we are finding $a_n=-3-2(n-1)$

16. egbeach

thank you!

17. freckles

and as you can see we get all the terms when pluggin n=1,2,3,... $a_1=-3-2(1-1) \\ a_1=-3-2(0) \\ a_1=-3 \\ a_2=-3-2(2-1) \\ a_2=-3-2(1) \\ a_2=-3-2 \\ a_2=-5$ and so on ,,,

18. freckles

we will find find that a_n=-3-2(n-1) that a_3=-7 and a_4=-9

19. freckles

and so on... `