Question

I've never seen a5 before!!!!!

What is the 7th term of the geometric sequence where a1 = -5 and a5 = -1,280? (3 points)
Answer

5,120

-5,120

20,480

-20,480

Answer 1

a5 means the 5th term.

Answer 2

oh:)

Answer 3

first find r=common ratio, using the formula,
\(\huge a_n=a_1r^{n-1}\)
n=5, a1=-5,a5=-1280

Answer 4

okay:)

Answer 5

what would i plug in for r into the equation?

Answer 6

you need to find 'r' from that equation, thats the only unknown variable.

Answer 7

n = 7 I thought

Answer 8

remember that you have the value of a5.
n will be 7 when you'll find the 7th term.
now you are finding r, using 5th term, so n= 5 first

Answer 9

oh alright

Answer 10

-5 x r ^(5-1)

Answer 11

-5^4?

Answer 12

no....
a5=-1280
so, -1280 = -5 r^4
try to isolate and find r from here.

Answer 13

first you can divide by -5 on both sides.

Answer 14

can you find r ?

Answer 15

let me try

Answer 16

-1280/5?

Answer 17

r^4 = -1280/ -5 =.... ?

Answer 18

256

Answer 19

yes, r^4 = 256, so r=.... ?

Answer 20

4294967296

Answer 21

:O
r^4 = 265
\(\large r = \sqrt[4]{256}=...\)
don't do 256^4

Answer 22

Oh really?? my error one sec

Answer 23

4 sqrt 256
= 4sqrt of (4^4)
= 4

Answer 24

not quite sure if that's correct

Answer 25

yes, r= 4 is correct.

Answer 26

oh okay good

Answer 27

ill plug it in

Answer 28

now you need 7th term
now take n = 7
r= 4
a1 =-5 as always.
plug these in
\[\huge a_n=a_1r^{n-1}\]

Answer 29

-5 x 4^ (5-1)

Answer 30

oh right!!! n= 7 this time

Answer 31

yes, because you are finding 7th term

Answer 32

-5 x 4= -20

i don't know how to plug the whole to the power of "(7-1)"

Answer 33

again!
don't do -5*4 first!!
^ has greater priority,
so do
4^{7-1} = 4^6 first
then multiply by 5

Answer 34

4^(7-1) = 4096

Answer 35

yes, 4096*(-5)= ?

Answer 36

-20480

Answer 37

you are \(\huge \color{red}{\checkmark}\)