Question

Will give medal and become fan!!!
Identify the 31st term of an arithmetic sequence where a1 = 26 and a22 = -226.
Answers
-274
-284
-334
-346

Answer 1

@bohotness @freckles @ganeshie8 @vera_ewing

Answer 2

@XoALIEoX

Answer 3

@StudyGurl14

Answer 4

@Holly00d1248

Answer 5

\[d=\frac{a_{22}-a_1}{22-1}=\]

Answer 6

d represents the common difference by the way

Answer 7

\[a_n=a_1+(n-1)d \text{ can be used to find } a_{31} \text{ once we find } a_1 \text{ and } d\]
So that is why I'm asking you to compute that above to find d

Answer 8

@freckles I dont understand?

Answer 9

which equation or formula do you now understand?

Answer 10

not*

Answer 11

@freckles I understand the equation but I can figure out how to work it

Answer 12

\[d=\frac{a_{22}-a_1}{22-1}= \]

the bottom equals 22-1=?
you are given the top numbers...a_(22)=-226 and a_1=26
so I mean a_(22)-a_1=-226-26=?

do find 22-1 all you do is think of having 22 somethings and 1 gets taken away
how many somethings do you have left?

Answer 13

to find -226-26
since both of them are negative you add 226 and 26
and then put a - on the sum when done

Answer 14

a21/21?

Answer 15

the bottom is right
but how do you just assume the difference of the 22nd term and the 1st is going to give you the 21st term ?

Answer 16

I think you would be better off by doing what I said

Answer 17

again you are given the 22nd term is -226
and the 1st term is 26

Answer 18

-252 which isnt in the answer choice

Answer 19

enter those numbers into the top in the respective spot

Answer 20

lol I didn't say that was an choise
I said we were trying to find d.
\[d=\frac{a_{22}-a_1}{22-1}=\frac{-226-26}{21}=\frac{-252}{21}\]

Answer 21

so now we have:
\[a_n=a_1+(n-1)d \\ \text{ where} a_1=26 \text{ and } d=\frac{-252}{21} \\ a_n=26+(n-1) \frac{-252}{21}\]
now to find the 31st term replace n with 31

Answer 22

idk how to do it!!!!!

Answer 23

-12

Answer 24

a1 = 26
a22 = –226
a22=a1+21d
Substitute!
-226=26+21d
21d=-252
d= -12
Now lets find the 31st term.
a31=a1+30d
a31=26+30 * (-12)
a31=26 + -360
a31= -334