Question

Write a formula for the nth term of the geometric sequence:
12, -3, 3/4, -3/16, ...

Answer 1

12/-3 =
-3/3/4=

Answer 2

Both are -4

Answer 3

-1/4

Answer 4

A geometric sequence is defined by \[a_n=a_1r^{n-1}\]\(a_1 = \text{1st term of series}\)\[r=\text{common ratio represented as} ~ \frac{a_{n+1}}{a_n}\]\[n=\text{number of terms}\]

Answer 5

So in finding \(r\), find the common ratio of... \[\frac{-3}{12}=~?\]\[\frac{\dfrac{-3}{4}}{-3}=~?\] etc.

Then what is the first term of your sequence? That would be \(a_1\).

Answer 6

12

Answer 7

Once you find these two values, just plug it back in to your formula and you'll have the general formula for the nth term of a geometric sequence.

Answer 8

I see what you did there. Okay, that makes a lot more sense, thank you.

Answer 9

OK, yes, \(a_1 = 12\). What is the common ratio now? Divide the preceding term by the term before it.

Answer 10

The common ratio was -4.

Answer 11

That is wrong, it's the second term/first term. Not the other way around.

Answer 12

0.25?

Answer 13

\(\color{red}{-}0.25~~ \text{or} ~-\frac{1}{4}\)

Answer 14

So you've got \(a_1=12\) and \(r=-\frac{1}{4}\), just plug this in to the formula to solve for \(a_n\).

Answer 15

So just plugging in 12 and -1/4 would give me the formula I need, And that would complete the answer?

Answer 16

Precisely.

Answer 17

Awesome, thank you!

Answer 18

No problem :)