Find a nth term for this sequence 1//1/3,1/9,1/15,1/21,1/27..
look at the denominators:
3,9,15,21,27, ...
so maybe 1/6n - 1/3
looks more like 1/(6n-3)
To find the nth term of the given sequence, let's first observe the pattern:
1/3, 1/9, 1/15, 1/21, 1/27, ...
We can see that the numerator of each term is always 1. However, the denominator follows a pattern: 3, 9, 15, 21, 27, ...
The pattern in the denominators is an arithmetic sequence with a common difference of 6. So, to find the nth term, denoted as Tn, of this sequence, we can use the formula for the nth term of an arithmetic sequence:
Tn = a + (n - 1) * d
In this case, the first term a is 3 (the denominator of the first term), and the common difference d is 6. Substituting these values into the formula, we can find the nth term:
Tn = 3 + (n - 1) * 6
Now, simplifying the expression:
Tn = 3 + 6n - 6
Tn = 6n - 3
Therefore, the nth term of the given sequence is 6n - 3.