SOLUTION: Good Morning, I would like some help in solving the following problem: Find the tenth term of the sequence 5, -25, 125, -625. Thank you in advance for your help. Denise

Algebra ->  Sequences-and-series -> SOLUTION: Good Morning, I would like some help in solving the following problem: Find the tenth term of the sequence 5, -25, 125, -625. Thank you in advance for your help. Denise      Log On


   

Question 131275: Good Morning, I would like some help in solving the following problem:
Find the tenth term of the sequence 5, -25, 125, -625. Thank you in advance for your help.
Denise
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If there were no minus signs in the sequence, it would
be 5%5E1,5%5E2,5%5E3,5%5E4, etc.
If n is the number of the term of the sequence, then
5%5En = 5, 25, 125, 625, etc.
Now to account for the minus sign, how do I get
1, -1, 1, -1, 1, etc. ?
%28-1%29%5E%28n%2B1%29 will do this, because
%28-1%29%5E2+=+1 (1st term)
%28-1%29%5E3+=+-1 (2nd term)
%28-1%29%5E4+=+1 (3rd term)
%28-1%29%5E5+=+-1 (4th term)
etc.
So, the sequence is
%28-1%29%5E%28n%2B1%29%2A5%5En= 5, -25, 125, -625, etc.
What is the 10th term? It is
%28%28-1%29%5E11%29%2A%285%5E10%29
Since -1 gets multiplied by itself an odd number of times,
(11 is odd), the answer will be negative
%28-1%29%2A%285%5E10%29+=+-9765625 by my calculator