Question

What is the next term in the sequence 2, 8, 32, 128, ...?

256
512
768
1024

Answer 1

Hey, P-G, step back a moment and ask yourself: how do we get from 2 to 8?
Then, how do we get from 8 to 32?

We're looking for a pattern that we will summarize in a simple formula for the terms of this sequence.

Answer 2

it would be 512. the pattern is the number gets multiplied by 4 to get the next number.

Answer 3

this seems like it's a geometric sequence because the sequence multiplies by 4 and geometric sequence use multiplication between the sequences.

2, *4 8, *4 32, *4 128, *4 ...?

Answer 4

This is clearly a geometric sequence as you can see that they're not increasing in a linear form, so because this is geometric you have to find the ratio, So you can divide any number by the previous number, so..

Answer 5

512

Answer 6

So, who can come up with a simple formula that works to predict the nth term of this sequence?

Answer 7

Mee!!

Answer 8

Go riiiiight ahead!
Thanks, Zale, for putting a name (geometric) to this sequence.

Answer 9

http://www.wolframalpha.com

Answer 10

they gave sequence when i plugged in numbers

Answer 11

2^1, 2^3, 2^5, 2^7, 2^9

Answer 12

f(n) = f(n – 1) • r, where n > 0

The rate is 4

Suppose you want to find the 5th term (you do >.> )

f(5) = f(5-1) * 4

f(5) = f(4) * 4

f(5) = 128

Answer 13

512 * typo >.<

Answer 14

f(4) = 128

128 * 4 = 512 :>

Answer 15

2^2n+1

Answer 16

As Zale has correctly pointed out, this is a geometric sequence. Have any of you seen the formula a*r^n (or a*r^(n-1)? Could that be used to write a simple formula with which to predict the nth value of the sequence?

Answer 17

You can also use, f(n) = f(n – 1) • r

Yes I've seen that formula :)

Answer 18

that's a recursion formula; each term depends on the value of the preceding one. Can anyone come up with a formula that's NOT a recursion formula?

Answer 19

f(n) = f(1) • r^n-1

Answer 20

Yes, or f(n)=2*(4)^(n-1). Agreed? With what value should n begin?

Answer 21

Your asking me? Or paris?