Question

PLEASE HELP I have tried to work it out but just cant...
What is the 32nd term of the arithmetic sequence where a1 = 13 and a13 = −59?

−185

−179

−173

−167

Answer 1

The nth term in general is

an = a1 + d(n-1)

where d is the common difference

Answer 2

i think 6 is the common difference...

Answer 3

a1 = 13 so,

an = a1 + d(n-1)

an = 13 + d(n-1)

Answer 4

-6 i mean

Answer 5

then we also know that a13 = -59 (ie the 13th term is -59)

an = 13 + d(n-1)

a13 = 13 + d(13-1) ... replace n with 13

-59 = 13 + d(13 - 1)

solving that for d gives you d = -6, correct

Answer 6

and then that is where i got stuck at...

Answer 7

so that means

an = a1 + d(n-1)

an = 13 + d(n-1)

an = 13 + (-6)(n-1)

an = 13 - 6n + 6

an = -6n + 19

Answer 8

an = -6n + 19 is the nth term formula that allows you to find any term

you want the 32nd term, so plug in n = 32 and evaluate

Answer 9

so a32+-6(32)+19=... right?

Answer 10

a32 = -6(32) + 19 I think you meant

Answer 11

yeah, my bad, i was pushing the shift key....

Answer 12

that's ok

Answer 13

now just evaluate -6(32) + 19

Answer 14

-211 is what i got... i did something wrong.

Answer 15

You should have gotten -173

Answer 16

alternatively, you can plug n = 32 into an = 13 + (-6)(n-1) to get

an = 13 + (-6)(n-1)

a32 = 13 + (-6)(32-1)

a32 = -173

Answer 17

hmm you must have done 6*32 + 19 and made the result negative

Answer 18

i got lost at the part where its a32=13+(-6)(32-1)... and yeah, i thought thats what i was supposed to do because () usually indicates *...

Answer 19

right? so what was i actually supposed to do for this equation? @jim_thompson5910

Answer 20

either equation works since

an = 13 + (-6)(n-1)

is equivalent to

an = -6n + 19

Answer 21

ohh, okay that makes much more since now!!

Answer 22

so instead of using () for multiplication, i use it for addition?

Answer 23

no it means multiplication

(-6)(n-1) means -6 times n-1

Answer 24

you may need to use the symbol * for multiplication

Answer 25

BEHHHH I HATE MATH~

Answer 26

yeah it's picky sometimes

Answer 27

yes! VERY! i think i may understand it...

Answer 28

that's great, glad you do