SOLUTION: find the nth term of the sequence -2/3,-1/6,1/3,5/6,4/3

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Question 1140358: find the nth term of the sequence -2/3,-1/6,1/3,5/6,4/3
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
-2%2F3......-1%2F6......1%2F3......5%2F6......4%2F3+
first find differences
........3%2F6......3%2F6......3%2F6......3%2F6
all differences same, means you have an arithmetic sequence with common difference d=3%2F6
since irst term is a%5B1%5D=-2%2F3, general formula for nth term will be
a%5Bn%5D=a%5B1%5D%2Bd%28n-1%29
a%5Bn%5D=-2%2F3%2B%283%2F6%29%28n-1%29-> nth term
check:
a%5B1%5D=-2%2F3%2B%283%2F6%29%281-1%29
a%5B1%5D=-4%2F6%2B%283%2F6%29%2A0
a%5B1%5D=-4%2F6+...simplify
a%5B1%5D=-2%2F3+

a%5B2%5D=-2%2F3%2B%283%2F6%29%282-1%29
a%5B2%5D=-4%2F6%2B%283%2F6%29
a%5B2%5D=-1%2F6+
a%5B3%5D=-2%2F3%2B%283%2F6%29%283-1%29
a%5B3%5D=-2%2F3%2B%283%2F6%292
a%5B3%5D=-2%2F3%2B1+
a%5B3%5D=1%2F3++
and so on

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Rewrite the given sequence all with the least common denominator:

-4/6, -1/6, 2/6, 5/6, 8/6, ...

The numerators form an arithmetic sequence: -4, -1, 2, 5, 8, ...

So the given numbers are the first 5 terms of an arithmetic sequence given by the formula

t%28n%29+=+%283n-7%29%2F6

However, while that is very probably the intended answer to the problem, in fact it is not possible to answer the question as posed. The trouble is that, with the problem as shown, the subsequent terms of the sequence could be ANYTHING; and of course that would make it impossible to know the n-th term.

Unfortunately, you see this kind of problem all the time, where there is an obvious apparent pattern to the given sequence of numbers. But for the problem to be valid and solvable, the statement of the problem HAS TO tell you that the sequence is an arithmetic sequence.