Question

What is a possible value for the missing term of the geometric sequence?

1,250, ___, 50,

Answer 1

Use \[ \Large a_1=a_nr^{n-1}\]
let \(a_1=1250\) then
\[\Large a_3=a_1q^2 \\
\Large 50=1250q^2 \]

Answer 2

wait im still kind of confused where do i plug in the values?

Answer 3

Well, can you evaluate q from what I have given you above? Pardon me by the way, you can set q=r for this, I am european, we set q rather than r for ratio. It means the same thing in the above.

Answer 4

\[\Large a_n=a_1r^{n-1} \] So, this time I wrote it better, you can see that when you choose various numbers for \(n\) you can derive all the necessary parts of the GP from the problem set.

Answer 5

So I assume that \(a_1\) is equal to the first part given above \(a_1=1250\) we want to figure out what \(a_2\) is, the blank spot above. We don't know that yet, however we can already write the formula down like this at the moment
\[\Large a_n = 1250r^{n-1} \]
So we need to figure out what r is in order to get to \(a_2\) we do that by computing \(a_3=50\)

\[\Large a_3=a_1r^2 \\ \Large 50=1250r^2 \]

Answer 6

oh okay so would i divide both sides? by 50

Answer 7

you want to solve for \(r\)

Answer 8

wait so im trying to isolate r?

Answer 9

As soon as you have \(r\) you can compute any number in the GP

Answer 10

yes, exactly. For any Geometric Problem, the ratio is important, that's all what it is about. A geometric progression is defined through the ratio, so as soon as you have found that ratio you're able to make forecasts about it.

Answer 11

oh okay so then how would i start off? im kind of new to this

Answer 12

would i square it since it's r^2?

Answer 13

\[\Large 50=1250r^2 \\
\Large r=\sqrt{\frac{50}{1250}}= \pm 0.2 \]

Answer 14

ohh 0.2? would be the answer, what formula is that?

Answer 15

The answer isn't given by r yet alone, you need to compute \(a_2\)

Answer 16

is 0.2 r? is that just the formula for finding r?

Answer 17

\[\Large a_n=1250\cdot (0.2)^{n-1} \]

Answer 18

So what is \(a_2\) ?

Answer 19

250?

Answer 20

i did 1250* 50

Answer 21

you plug in a two into the equation above, that gives you your answer.

Answer 22

so how would i set that up? 150 x 2? or am i wrong

Answer 23

250 yes.

Answer 24

excuse me that I didn't agree before, I was distracted.

Answer 25

I missed your reply above.

Answer 26

oh okay thankkkk youu so much! :)

Answer 27

you're welcome