SOLUTION: What are the first four terms of the following sequence: an = (-3)^n for n ≥ 1? A) 0, -3, 18, -81 B) -3, 18, -81, 324 C) 3, 18, 81, 324 D) 18, -81, 324, -1215

Algebra ->  Sequences-and-series -> SOLUTION: What are the first four terms of the following sequence: an = (-3)^n for n ≥ 1? A) 0, -3, 18, -81 B) -3, 18, -81, 324 C) 3, 18, 81, 324 D) 18, -81, 324, -1215      Log On


   



Question 1082980: What are the first four terms of the following sequence: an = (-3)^n for n ≥ 1?
A) 0, -3, 18, -81
B) -3, 18, -81, 324
C) 3, 18, 81, 324
D) 18, -81, 324, -1215

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
a%5Bn%5D+=+%28-3%29%5En

We begin by plugging in 1 for n:

a%5B1%5D+=+%28-3%29%5E1
a%5B1%5D+=+-3   <-- so the only possible correct choice 
so far is C, for none of the others have 1st term -3

But to make sure, let's plug in 2 for n:

a%5B2%5D+=+%28-3%29%5E2
a%5B2%5D+=+9

Uh oh!  Something's wrong!  The second term has to be 9, and
none of the choices have 2nd term 9.

Let's see what the correct answer would have to be.

Let's plug in 3 for n:

a%5B3%5D+=+%28-3%29%5E3
a%5B3%5D+=+-27  

Let's plug in 4 for n:

a%5B4%5D+=+%28-3%29%5E4
a%5B1%5D+=+81

So the correct answer is

-3, 9, -27, 81

So it's none of those listed.

Edwin