SOLUTION: Please help me with problem, thanks: 7+(-21)+63+(-189)+... a) n=18 b) S_n=3829

Algebra ->  Sequences-and-series -> SOLUTION: Please help me with problem, thanks: 7+(-21)+63+(-189)+... a) n=18 b) S_n=3829      Log On


   

Question 607821: Please help me with problem, thanks:
7+(-21)+63+(-189)+...
a) n=18
b) S_n=3829
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi

Geomtric sequence: a%5Bn%5D+=+a%5B1%5D%2Ar%5E%28n-1%29

{7+(-21)+63+(-189)+...}

Note the Change of sign:

a%5Bn%5D+=+7%2A%28-3%29%5E%28n-1%29

a%5B18%5D+=+7%2A%28-3%29%5E%2817%29=+highlight%28903981141%29

  

 7/4(1-r^n) = 3829

  (1-(-)3^n) = (4/7)3829 = 2188

     3^n = 2187

       n = 7