Question

what is the value of a1 for a geometric sequence with a4=40 and a6=160

a-2
b-5
c-8
d-10

Answer 1

Hints:

a5 = a4*r

a6 = a5*r ---> a6 = (a4*r)*r

Answer 2

a6 = (a4*r)*r turns into a6 = a4*r^2

Answer 3

because a6 = a4*r^2, a4=40 and a6=160, we can say


a6 = a4*r^2
160 = 40*r^2
r = ???

Answer 4

What does r stand for

Answer 5

r is the common ratio

Answer 6

duh

Answer 7

so the common ratio is what?

Answer 8

if you have the fourth term a4, you multiply that fourth term by r to get the fifth term

this applies in general to any term (not just the 4th term)

Answer 9

here's an example of a geometric sequence

1, 2, 4, 8, 16, 32

Notice how each term is multiplied by 2 to get the next one (eg: 4 ---> 8, 8 = 4*2)

Answer 10

so in my example, r = 2

Answer 11

Ok so the common ratio in my problem is 2?

Answer 12

no, that's for my example

Answer 13

I don't know what your common ratio r value is yet

Answer 14

I know, i realized i made a mistake when i posted that one

Answer 15

you have to solve 160 = 40*r^2

Answer 16

How do i find the common ratio for that

Answer 17

nevermind

Answer 18

Solving 160 = 40*r^2 gives you r = ???

Answer 19

wouldnt it be 2?

Answer 20

yeah it's actually 2

it's a coincidence that I used 2 as well

Answer 21

Ok thats what i thought haha

Answer 22

Now we use the formula

\[\Large a_{n} = a*(r)^{n-1}\]

Answer 23

plug in n = 4, r = 2 to get

\[\Large a_{n} = a*(r)^{n-1}\]

\[\Large a_{4} = a*(2)^{4-1}\]

Then plug in \(\large a_{4} = 40\) to get

\[\Large 40 = a*(2)^{4-1}\]

now solve for 'a'

Answer 24

Ok now i can plug in one of a b c or d

Answer 25

ok

Answer 26

you could, but solving is more direct

Answer 27

I recommend doing it this way because you shouldn't be dependent on multiple choice. What if this was a free response or fill in the blank problem?

Answer 28

Good point

Answer 29

I guess though, having multiple choice there means you should take advantage of it to save time. So you should know how to do it both ways.

Answer 30

So its b

Answer 31

5

Answer 32

correct

Answer 33

that's 'a' or a1

Answer 34

Sweet
thanks

Answer 35

you're welcome