1/6,1/2,5/6,.......
What is the general term for this?
it's a sequence. It looks like the nth term is the nth odd number divided by 6:
1/6, 3/6, 5/6, 7/6, ...
or, symbolically,
Tn = (2n-1)/6
specifically, this would be an arithmetic sequence, where the difference between terms is a constant, in this case 2/6, or 1/3.
To find the general term for a sequence, we need to observe the pattern in the given terms.
Looking at the sequence 1/6, 1/2, 5/6, we notice that each term is obtained by adding 2/3 to the previous term.
So, starting with the first term, 1/6, if we add 2/3, we get the second term:
1/6 + 2/3 = 1/6 + 4/6 = 5/6
Similarly, adding 2/3 to the second term gives us the third term:
1/2 + 2/3 = 3/6 + 4/6 = 7/6
Therefore, we can conclude that the general term for the sequence is obtained by adding 2/3 to the previous term.
In mathematical notation, we can express this as:
a(n) = a(n-1) + 2/3
where a(n) represents the nth term of the sequence and a(n-1) represents the (n-1)th term.