SOLUTION: Please Help: Find the indicated term of the geometric sequence. a = -3, r = -4; Find the 7th term. A) 3072 B) 196,608 C) -4096 D) -12,288

Algebra ->  Sequences-and-series -> SOLUTION: Please Help: Find the indicated term of the geometric sequence. a = -3, r = -4; Find the 7th term. A) 3072 B) 196,608 C) -4096 D) -12,288       Log On


   

Question 201924: Please Help:
Find the indicated term of the geometric sequence.
a = -3, r = -4; Find the 7th term.
A) 3072
B) 196,608
C) -4096
D) -12,288
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The general form of ANY geometric sequence is a%5Bn%5D=a%2Ar%5E%28n-1%29 where "n" starts at 1 (the formula is slightly different if you start at different "n" values)



a%5Bn%5D=a%2Ar%5E%28n-1%29 Start with the given equation.


a%5Bn%5D=-3%2A%28-4%29%5E%28n-1%29 Plug in a=-3 and r=-4 (these values are given)


a%5B7%5D=-3%2A%28-4%29%5E%287-1%29 Plug in n=7 (for the 7th term)


a%5B7%5D=-3%2A%28-4%29%5E6 Subtract


a%5B7%5D=-3%2A4096 Raise -4 to the 6th power to get 4,096


a%5B7%5D=-12288 Multiply



So the 7th term is -12,288 which means that the answer is D)