SOLUTION: Find the formula for the nth term of the geometric sequence with a base 2= -18 and a base 5= 144

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: Find the formula for the nth term of the geometric sequence with a base 2= -18 and a base 5= 144      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1087012: Find the formula for the nth term of the geometric sequence with a base 2= -18 and a base 5= 144
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
a%5B2%5D = a%5B1%5D%2Ar = -18,

a%5B5%5D = a%5B1%5D%2Ar%5E4 = 144.


====>  a%5B5%5D%2Fa%5B2%5D = r%5E3 = 144%2F%28-18%29 = -8  ====>  r = -2.


Thus we found that the common ratio of the progression is -2.


Then a%5B1%5D = %28-18%29%2F%28-2%29 = 9.


The progression is 9, -18, 36, -72, 144 . . . 


The formula for the n-th term is 


a%5Bn%5D = 9%2A%28-2%29%5E%28n-1%29,  n = 1, 2, 3, . . .


See introductory lessons on geometric progressions in this site:
    - Geometric progressions
    - The proofs of the formulas for geometric progressions
    - Problems on geometric progressions
    - Word problems on geometric progressions


Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Geometric progressions".