SOLUTION: find the common ratio, explicit formula, and the recursive formula a4 = -1/4 and a1 = 2

Algebra ->  Sequences-and-series -> SOLUTION: find the common ratio, explicit formula, and the recursive formula a4 = -1/4 and a1 = 2      Log On


   

Question 1181078: find the common ratio, explicit formula, and the recursive formula
a4 = -1/4 and a1 = 2
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.
find the common ratio, explicit formula, and the recursive formula
a4 = -1/4 and a1 = 2
~~~~~~~~~~~~~~~~ 

    a%5B4%5D = a%5B1%5D%2Ar%5E3


    -1%2F4 = 2%2Ar%5E3


    r%5E3 = %28%28-1%2F4%29%29%2F2 = -1%2F8


    r = root%283%2C-1%2F8%29 = -1%2F2.    (the common ratio).             ANSWER


Recursive formula  a%5Bn%2B1%5D = %28-1%2F2%29%2Aa%5Bn%5D.                    ANSWER


Explicit formula   a%5Bn%5D = 2%2A%28-1%2F2%29%5E%28n-1%29 = %28-1%29%5E%28n-1%29%2F2%5E%28n-2%29.     ANSWER

Solved.