Question

Write the explicit formula that represents the geometric sequence -2, 8, -32, 128

Answer 1

Have you found the common ratio yet?

Answer 2

No

Answer 3

What do you multiply -2 by to get 8?

Answer 4

@KimJaFo

Answer 5

8

Answer 6

I mean 4

Answer 7

-4, I think.

Answer 8

What do you multiply 8 by to get -32

Answer 9

-4

Answer 10

And, to get 128, you multiply -32 by -4.

So, the common ratio seems to be -4

Answer 11

Yes

Answer 12

Do you have answer options? If so, we can test them against the terms of the sequence.

Answer 13

No, I don't sadly. Thats why im having trouble with it.

Answer 14

To get the signs to alternate, we will have to use (-1)^n where n is an integer >0.

So, if n = 1, then (-1)^n will = -1.

If n = 2, then (-1)^n will - + 1

That makes the signs alternate negative, positive, negative, positive and so on.

Answer 15

Now, for the value of the terms: -2, 8, -32, 128

Would you write them as powers of 2?

Ignore the signs for now.

For example, 2 = 2^1 and 8 = 2^3

You do 32 and then 128 as powers of 2, okay?

Answer 16

okay