SOLUTION: Write an explicit formula for the sequence determined by each recursion formula. 1)t₁ = 1; tn = tn-1 -4 2)t₁ = 20; tn = (-1/2)tn-1 Thank you.

Algebra ->  Sequences-and-series -> SOLUTION: Write an explicit formula for the sequence determined by each recursion formula. 1)t₁ = 1; tn = tn-1 -4 2)t₁ = 20; tn = (-1/2)tn-1 Thank you.       Log On


   

Question 1037881: Write an explicit formula for the sequence determined by each recursion formula.
1)t₁ = 1; tn = tn-1 -4
2)t₁ = 20; tn = (-1/2)tn-1
Thank you.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
1) t%5B1%5D=1 , t%5Bn%5D=t%5Bn-1%5D-4
That is an arithmetic sequence with first term 1 , and common difference d=-1 .
For arithmetic sequences the explicit formula is
t%5Bn%5D=t%5B1%5D%2Bd%28n-1%29 .
For the particular arithmetic sequence in this problem,
highlight%28t%5Bn%5D=1-4%28n-1%29%29 .

2) t%5B1%5D=20 , t%5Bn%5D=%28-1%2F2%29t%5Bn-1%5D
That is a geometric sequence with first term 20 , and common ratio r=-1%2F2 .
For geometric sequences the explicit formula is
t%5Bn%5D=t%5B1%5D%2Ar%5E%28n-1%29 .
For the particular arithmetic sequence in this problem,
highlight%28t%5Bn%5D=20%2A%28-1%2F2%29%5E%28n-1%29%29 .