General term of the sequence -1/2, 1, -7/8, 10/6...?
Anybody see a pattern?
- Nancy CLv 48 years agoFavourite answer
If the last term is actually 10/16 rather than 10/6, then here is the pattern:
Rewrite the second term as 4/4.
Then the sequence is -1/2.4/4,-7/8,10/16, ...
The numerators form an arithmetic sequence 1, 4, 7, 10, ... with a common difference of 3. The general term for the numerators can be found using the formula a+(n-1)(d) where a is the first term.
So for the numerators, the general term is
The denominators form a geometric sequence -2, 4, -8, 16, ...with common ratio r =-2.
The general term of a geometric sequence can be found using the formula ar^(n-1).
So for the denominators, the general term is
Putting this together, the general term for your sequence is