Question

What is a possible value for the missing term of the geometric sequence?
37, ___, 925...?
a. -185
b. -4,625
c. -925
d. 481
The answer is obviously d. correct? I feel like this is a trick question, not to sure.

Answer 1

why obviously???

Answer 2

I figured that it couldn't be a negative lol

Answer 3

Its A

Answer 4

Nah it cld be

Answer 5

tell me how c:<

Answer 6

I just taught this today

Answer 7

Ok we know that we start off with our first term, called "a"
In this case a=37

Answer 8

Indeed

Answer 9

Then subsequently we keep multiplying the previous term by a constant
We are not given the constant

Answer 10

But the constant is known as r

Answer 11

so our first term is
\[ \{ a, a*r, a*r*r, a*r*r*r, ...\}\]
which in other words is
\[ \{a,ar,ar^2,ar^3,ar^4,,,\}\]

Answer 12

You familiar with this?

Answer 13

Hmm I'm just learning this, but I get what you're saying.

Answer 14

SO in our case we have the first term is 37 second is unknown and third term is 925
so a=37, ar=37*r and ar^2=925

Answer 15

Ok I get what you're saying..

Answer 16

so ar^2=925
we know that a=37
so \(37*r^2=925\)
\[ r^2=\frac{925}{37}\]

Answer 17

so \[r^2=25\]
\[\sqrt{r^2}=\sqrt{25}\]
r=5

Answer 18

So now we found out that r=5

Answer 19

So its easy to find the terms

Answer 20

First term is "a" which equals 37
Second term is a*r=37*5=q85
and the third term is ar^2=37(5)^2=925

Answer 21

So we see that our second term is 185

Answer 22

Basically really r is really -5
a=37
a*r=37(-5)=-185
a*r*r=37(-5)(-5)=925

Answer 23

Is this an online course?

Answer 24

Yes mam, it is, and thank you Rach c: but one more question. Why is it negative?

Answer 25

GONNAAA KILLL YOU :P

Answer 26

Lmao cx is there a reason though? hahaha

Answer 27

Ok i was showing you that the answer can be negative or positive in reality

Answer 28

ohhhh i see now lol thanks hahah cx

Answer 29

Ya rightttt :PPP I can show you an example if you would like

Answer 30

lol no I'm serious hahaha, i understood your method! I just didn't know why it was negative lol

Answer 31

Okkk lemme show u an example real quick

Answer 32

Of course :3

Answer 33

And thanks c:

Answer 34

Ok so lets take this example where our starting term a=37 and the multiplying constant is -5
Please list the first 5 terms of the sequence

Answer 35

Ok so 37, 185, 925, 4625, 23125 correct?

Answer 36

Nahhh remember its -5

Answer 37

Take the sign into account

Answer 38

My bad, 37, -185, 925, -4625, 23125, is this better?

Answer 39

Yupppp
Now refer back to the question above

Answer 40

So the answer is a. :3

Answer 41

Is that what you're asking me?

Answer 42

Yaaaaaa

Answer 43

The answer can technically be 185 or -185 but since they only gave the option of -185 we chose that

Answer 44

Ok i see whatchu mean B) Thanks a lot Rachel c:

Answer 45

Okkk Im out for now but i may be back later

Answer 46

Ok Love You

Answer 47

Awwwww ♥

Answer 48

Lol cx