Question

How do you find the common difference in an arithmetic sequence?
Here's an example:
Identify the 31st term of an arithmetic sequence where a1 = 26 and a22 = -226.

Answer 1

use the n'th term formula
\(\Large a_n = a_1 +(n-1)d\)

here, n = 22
a1 = 26
and a22 = -226
just plug them in! only 'd' = common difference is unknown

Answer 2

yeah, I know how to do that.. it's just the common difference that throws me off. how do you find that?

Answer 3

\(-226 = 26 + (22-1) d\)
find 'd' from here
thats your common difference :)

Answer 4

wait I thought the equation would be:
n=31
a1= 26

Answer 5

so it would a31=26+(31-1)d

Answer 6

thats correct equation, but you will need to find 'd' first for that , isn't it ?

Answer 7

yeah, that's what was throwing me off

Answer 8

\(-226 = 26 + (22-1) d\)
please first find 'd' from here...

Answer 9

i got that equation using the n'th term formula only

Answer 10

I got -4.8

Answer 11

is it ?

21d= -226 -26

i get d =12.....

Answer 12

oh I didn't switch around the equation. I got that now

Answer 13

now that you have d=12
use the equation you have for a31 :)

Answer 14

oh, and sorry, d should be -12
\(\Large d = -12 \)

Answer 15

let me work it out see if I have anymore questions

Answer 16

i got -334, which is one of my answer choices. thank you for helping me figure this out!!

Answer 17

-334 is correct :)
and welcome ^_^

Answer 18

while you're learning this topic, you can go through this....might be helpful :)
http://openstudy.com/study#/updates/503bb2a0e4b007f9003103b0