## anonymous one year ago 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

1. anonymous

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?

2. anonymous

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

3. anonymous

Correct (:

4. anonymous

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

5. anonymous

the answer is C

6. anonymous

I would think so.

7. anonymous

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

8. idku

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

9. idku

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.... $$a_1 \times r^{n-1} = a_n$$

10. idku

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: $$(-8) \times (-3)^{1000-1} = a_{1000}$$ $$\color{blue}{(-8) \times (-3)^{999} = a_{1000}}$$

11. anonymous

OH. Cool.