Question

My answer is B

What is the 8th term of the geometric sequence -1, 4, -16, ? (3 points)
Answer

16,384

-4,096

4,096

-16,384

Answer 1

What pattern have you identified?

Answer 2

12

Answer 3

I'm not sure what you mean by that. We can worry about the negatives after, but how did you get from 1 to 4 to 16? What is the pattern there?

Answer 4

16 - 4

Answer 5

Ok. So one possible pattern would be, to get from 4 to 16 you have to add 12. So compare that to the first two numbers, 1 to 4. 1 + 12 = 13. So that's not the right pattern. How else can you get from either 1 to 4 or from 4 to 16? (do one of them and check with the other)

Answer 6

you can subtract?

Answer 7

a1 = -1

Answer 8

i got 16,384

Answer 9

Two of the most common types of patterns are:L
1) adding/subtracting the same amount each time (called arithmetic).
eg. 2 4 6 8 10 ... or 10 9 8 7 ...
2) multiplying or dividing by the same amount each time (called geometric)
eg. 2 4 8 16 32 or 100 50 25 12.5 ...

Answer 10

That might be right, but we need to figure out how you got it to know if it is or not.

You tried the adding/subtracting way and it didn't work. What about multiplication? What would you have to multiply by 1 to get to 4?

Answer 11

1 x 4

Answer 12

Good. So if that's right than multiplying the second number by 4 will get you the third.

4 x 4 = 16.

Looks about right, what would the 4th term be?

Answer 13

16 x 4?

Answer 14

64

Answer 15

ohh i get it

Answer 16

Excellent. It is easier to see a kind of formula for later terms if you write each term as a power of 4, rather than the actual number. So the pattern is the same as 4^0, 4^1, 4^2, .... which would make the 8th term be?