Question

help? i keep getting the wrong answer?


What is the 32nd term of the arithmetic sequence where a1 = –32 and a9 = –120? (1 point)


–384
–373
–362
–351

Answer 1

Can you show us your working?

Answer 2

@FaiqRaees im using
an = a1 + (n - 1)d
a32 = -32 + (-120 - 1)d but i dont know what to put in place of d

Answer 3

i actually know why i was getting the wrong answer at first but i cant get past here

Answer 4

Okay so you are mistaking things
N is not equal to a term in the series. It describes the position of the number in a series
D is the difference between term
a1 implies first term, a2 the second term and so on

So your first task is to find the difference.
try finding it out by plugging a9 and a1 in the formula

Answer 5

aN is the number of your choice from the sequence.

Answer 6

@FaiqRaees in this case shouldnt it be 32 since thats the number youre trying to find in the sequence?

Answer 7

Yes true, but if we directly start with a32, we have to account for the unknown value of 'd'. So first we have to figure out the value of 'd' : difference

Answer 8

@FaiqRaees aaaah i see what youre sayin now. so what do you need to find the difference between??

Answer 9

\[\large\rm a_9=a_1(n-1)d\ \]

Answer 10

@FaiqRaees so would i substitute into that equation? so a9 = -32 (9 - 1)d ???

Answer 11

You have the value of a9 right? Use that and find out the difference

Answer 12

@FaiqRaees oh oops so -120 = -32 (-120 - 1)d ??? idk if thats right though because every time i work it out i get some long decimal

Answer 13

What is the value of 'n' here?

Answer 14

@FaiqRaees n would be a9 wouldn't it? since you said it wasnt the number were looking for

Answer 15

n is the term number

Answer 16

Still confused?

Answer 17

you use
\[ a_n = a_1 + (n - 1)d \]
you have to be meticulous (careful).
they give you \(a_9\) which is associated with n=9 (the n comes from the 9 in a9)
so using a1 = –32 and a9 = –120
we use n=9, and
-120= -32+(9-1)*d
can you "solve for d" ?

Answer 18

@phi @FaiqRaees oh ok that makes sense um so d=5?

Answer 19

No d is not 5. Can you show the working for d?

Answer 20

@FaiqRaees ah dang sorry im so bad at math omg its so embarrassing im always screwing things up ughgghhg
-120 = -32 + (9 - 1)d
-120 = -32 + (8)d
-120 = -24d
5 = d
im sorry

Answer 21

-120= -32+(9-1)*d

first simplify 9-1 to 8
-120 = -32+8d
now add +32 to both sides. then simplify both sides.

Answer 22

your work looks good except you -32+8d is not -24d
for the time being, just believe that, and instead, add +32 to both sides

Answer 23

@phi so -120 = -32 + 8d
-88 = 8d ???

Answer 24

yes. now divide both sides by 8
\[ \frac{-88}{8}= \frac{8}{8}d \]

Answer 25

@phi d = -11??

Answer 26

Correct

Answer 27

yes

now the formula is
\[ a_n= -32+ (n-1)\cdot -11 \]

Answer 28

Now you have a1 and difference.
Try finding out the value of a32

Answer 29

can you find a32 ? (i.e. use n=32)

Answer 30

@phi @FaiqRaees so would a32 = -374 ??

Answer 31

-373, do you mean?

Answer 32

did you do
a32= -32 + -11*(32-1)
= -32 + -11*31
= -32 - 341
= -373

Answer 33

btw, if you have time, see
https://www.khanacademy.org/math/algebra-basics/core-algebra-linear-equations-inequalities/core-algebra-solving-basic-equations/v/equations-2
for how to do the algebra. Your life will be easier if you learn how to do that.

Answer 34

@phi oh i got 342 instead of 341 for some reason :/

Answer 35

did you do -11*32 by hand or with a calculator?

Answer 36

* I mean -11*31

Answer 37

@phi by a calculator but i typed it in wrong i see where i messed up oops