Question

Given the following geometric sequence, find the 12th term: {2, -4, 8, ...}.

Answer 1

2 times what = -4?

-2 does

-2 x 2 = -4

-4 time what = 8?

Again, -2.

-2 x -4 = 8

You could do this over and over again or make a table, or you can make a function.

f(n) = f(1) • r

f(1) in this case is 2.

f(n) = 2 • r

r is rate of change, which is -2.

f(n) = 2 • -2

To find the 12th number in the sequence, just substitute n for 12.

f(12) = 2 • -2

f(12) = 2 • -2

-2^11 = -2048

2 x -2048 = -4096

So the 12th number in the sequence will be -4096.

Answer 2

2 times what = -4?
-2 does
-2 x 2 = -4

-4 time what = 8?
Again, -2.
-2 x -4 = 8

You could do this over and over again or make a table, or you can make a function.
f(n) = f(1) • r
`^(n-1)`
f(1) in this case is 2.
f(n) = 2 • r
`^(n-1)`
r is rate of change, which is -2.
f(n) = 2 • -2
`^(n-1)`
To find the 12th number in the sequence, just substitute n for 12.
f(12) = 2 • -2
`^(12-1)`
f(12) = 2 • -2
`^(11)`
-2^11 = -2048
2 x -2048 = -4096
So the 12th number in the sequence will be -4096.