SOLUTION: Write the nth term of the geometric sequence as a function of n. {{{ a[1] = -3}}} , {{{a[k+1] = -4a[k]}}}

Algebra ->  Sequences-and-series -> SOLUTION: Write the nth term of the geometric sequence as a function of n. {{{ a[1] = -3}}} , {{{a[k+1] = -4a[k]}}}      Log On


   



Question 973875: Write the nth term of the geometric sequence as a function of n.
+a%5B1%5D+=+-3 , a%5Bk%2B1%5D+=+-4a%5Bk%5D

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Write the nth term of the geometric sequence as a function of n.
+a%5B1%5D%22%22=%22%22+-3 , a%5Bk%2B1%5D%22%22=%22%22-4a%5Bk%5D
Substitute n=1

a%5B1%2B1%5D%22%22=%22%22-4%28-3%29
a%5B2%5D%22%22=%22%2212

So the common ratio is a%5B2%5D%2Fa%5B1%5D%22%22=%22%2212%2F-3=-4

nth term:

a%5Bn%5D%22%22=%22%22a%5B1%5Dr%5E%28n-1%29

a%5Bn%5D%22%22=%22%22-3%2A%28-4%29%5E%28n-1%29

Edwin