SOLUTION: I am trying to find the explicit formula for the following sequence: -2 1/2, -2, -1 1/2, -1, -1/2 In this problem, -2 1/2 corresponds to the term 1, -2 corresponds to the ter

Algebra ->  Sequences-and-series -> SOLUTION: I am trying to find the explicit formula for the following sequence: -2 1/2, -2, -1 1/2, -1, -1/2 In this problem, -2 1/2 corresponds to the term 1, -2 corresponds to the ter      Log On


   

Question 196139: I am trying to find the explicit formula for the following sequence:
-2 1/2, -2, -1 1/2, -1, -1/2
In this problem, -2 1/2 corresponds to the term 1, -2 corresponds to the term 2, -1 1/2 corresponds to the term 3, and so on. I've been working on this problem for over an hour and have tried lots of different formulas, but none work. Please help.
Thank you so much.
Found 2 solutions by Earlsdon, Edwin McCravy:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Have you tried:
a%5Bn%2B1%5D=%28a%5Bn%5D%2B0.5%29

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Edwin's solution:
a%5B1%5D=-2%261%2F2, a%5B2%5D=-2, a%5B3%5D=-1%261%2F2, a%5B4%5D=-1, a%5B5%5D=1%2F2,...

It is an arithmetic sequence because obviously 1%2F2 is 
being added to each term to get the next term.  Therefore
the common difference is d=1%2F2.

The nth term of an arithmetic sequence is given by the
formula:

a%5Bn%5D=a%5B1%5D%2B%28n-1%29d

So, upon substituting:

a%5Bn%5D=%28-2%261%2F2%29%2B%28n-1%29%281%2F2%29

Change the mixed fraction -2%261%2F2 
to the improper fraction -5%2F2

a%5Bn%5D=-5%2F2%2B%28n-1%29%281%2F2%29

Multiply through by 2 to clear of fractions:

2a%5Bn%5D=-5%2B%28n-1%29%2A1

2a%5Bn%5D=-5%2Bn-1

2a%5Bn%5D=n-6

Divide both sides by 2

a%5Bn%5D=%28n-6%29%2F2 

Edwin