Question

What is the 32nd term of the arithmetic sequence where a1 = 12 and a13 = −60?
@ganeshie8
−192

−186

−180

−174

Answer 1

whats the general term of arithmetic sequence ?

Answer 2

\(a_n = a_1 + (n-1)d\)

Answer 3

12+(32-1)d

Answer 4

yes, we need d :)

we're given :-
\(a_1 = 12\)
\(a_{13} = -60\)

\(-60 = 12 + (13-1)d\)
find \(d\) first

Answer 5

^^solve d

Answer 6

124d=-60 am i in the right direction

Answer 7

how ?

Answer 8

\(-60 = 12 + (13-1)d\)

\(-60 = 12 + (12)d\)

\(-72 = (12)d\)
solve d

Answer 9

d(13-1) i used distributive property then minused and they equaled 12d

Answer 10

-6? @ganeshie8

Answer 11

yes ! d = -6

Answer 12

ok now i just do that for 32

Answer 13

?

Answer 14

so, we have \(a_1 = 12\) and \(d = -6\)
we can find \(a_{32}\) using the general term formula ?

Answer 15

whats the formula

Answer 16

\(a_n = a_1 + (n-1)d\)

\(a_{32} = a_1 + (32-1)d\)

Answer 17

a1 is 12 and -6 is d

Answer 18

plug them and simplify

Answer 19

i got -2.583 i know that is wrong :(

Answer 20

@ganeshie8

Answer 21

\(a_n = a_1 + (n-1)d\)

\(a_{32} = a_1 + (32-1)d\)

\(a_{32} = a_1 + (31)d\)

Answer 22

plugin a1 and d values, and show me next step :)

Answer 23

step by step ok

Answer 24

a_32=12+(31d)

Answer 25

then i minused 12 from both sides

Answer 26

nope. first plugin the value for d also

Answer 27

12-186

Answer 28

a_32=-174

Answer 29

!!!omg I think I got it

Answer 30

\(a_{32} = a_1 + (31)d\)

plugin a1 and d values above

\(a_{32} = 12 + (31)(-6)\)
\(= 12 - 186\)
\(=-174\)

Answer 31

Yes :)

Answer 32

You are awesome thank you!!!11

Answer 33

np you're awesome too :D