Question

Find the next three terms of the sequence –8, 24, –72, 216, . . .

A) 648, –1944, 5832
B) 248, –616, 248
C) –648, 1944, –5832
D) 216, –648, 1944

Answer 1

Okay. This is probably an awful way to teach this, but this is how I learned.

–8, 24, –72, 216, . . .

What I would do is I would first divide 24 and -8

You would get -3.

Then try it.

-8 x -3 = 24

24 x -3 = -72

Do you understand?

Answer 2

Yeah so like the number is -3 and -8*-3 = 24 and 24*-3 = -72 and -72*-3= 216 and so on.. @elite.weeaboo

Answer 3

Correct (:

Answer 4

216*-3= -648, -648*-3= 1944, 1944*-3= -5832

Answer 5

the answer is C

Answer 6

I would think so.

Answer 7

Wait until idku is done typing. I could be wrong.

Answer 8

Oh, no it is correct, i was just going to make a definitional [ost.

Answer 9

just a brief post about the definitions:

A sequence that follows such a pattern (multiplying a term times some number to find the next term), is called a "geometric sequence".

This number -3, is the number by which you multiply to find the next term - and it is called "common ratio" (denoted by letter r).
So you can say in your case "r=-3"

\(a_1\) is a notation for the first term
\(a_2\) is a notation for the second term
\(a_3\) is a notation for the third term
so on.....
\(a_n\) is a notation for some \(\rm n\)th term

So in a geometric sequence (like yours) you should see that:
\(a_1 \times r = a_2\)
agree?

\(a_2 \times r = a_3\) or \(a_1 \times r \times r ~~= a_1 \times r^2= a_3\)
agree?

\(a_3 \times r = a_4\) or \(a_1 \times r \times r \times r~~= a_1 \times r^3= a_4\)

and thus....
\(a_1 \times r^{n-1} = a_n \)

Answer 10

So if you wanted to find 1000th term of your sequence, you would go:

\(a_1 \times r^{n-1} = a_n \)

\(a_1 \times r^{1000-1} = a_{1000} \)

your first term is -8, so:

\((-8) \times r^{1000-1} = a_{1000} \)

your common ratio is -3:

\((-8) \times (-3)^{1000-1} = a_{1000} \)

\(\color{blue}{(-8) \times (-3)^{999} = a_{1000}} \)

Answer 11

OH. Cool.