Question

PLEASE HELP I WILL AWARD MEDAL!!!!!!!!!!!!!!!!!!!!!!!!!

Identify the 31st term of an arithmetic sequence where a1 = 26 and a22 = –226.

–334

–274

–284

–346

Answer 1

@whpalmer4

Answer 2

@Hero

Answer 3

You need this relation between the first term and the n'th term of an arithmetic sequence:
\[\Large a_n = a_1+(n-1)d\]

Answer 4

Most importantly, you need the common difference d.
You are given the first term \(a_1\) and the 22nd term \(a_{22}\)
So plugging them in, can you solve for d?

Answer 5

So the answer is please????

Answer 6

Let's see. Plug them in first,
replace \(a_n\) with \(a_{22}=-226\)
replace \(a_1\) with 26
and of course, \(n = 22\)

And solve for d.

Answer 7

Thank you so much.

Answer 8

?
So what is your common difference \(d=\color{red}?\)

Answer 9

Oh I thought that the 22 was the answer.

Answer 10

No.

Answer 11

Did you even read my post? lol
22 is not the answer, but it will help...
Just plug it into the n-value, along with the rest, in the equation \[\Large a_n = a_1+(n-1)d\]

Answer 12

Yes I did read your post.

Answer 13

Great :)
Now please solve for \(d\) and tell me what you get.

Answer 14

it is hard to solve for d.

Answer 15

It isn't?
\[\Large -226 = 26+(22-1)d\]
There, now solve :)

Answer 16

d=-12

Answer 17

That wasn't so bad, now was it?
Now use this formula again, \[\Large a_n = a_1+(n-1)d\]

but this time, \(\large a_n = a_{31}\) (ie, we need the 31st term)
So with \(\large n = 31\)

and this time, you know d = -12

Answer 18

So how do we do this.

Answer 19

Same with the other one. Plug in the known values and solve.

Answer 20

It'd be nice if you show your steps too.

Answer 21

Ok so it is -334

Answer 22

There you go.
Aren't you glad you solved this yourself? :P

Answer 23

YES I AM SO GLAD YOU WERE SO HELPFULL