Question

1/4, 2/4, 3/4, 4/4,... write a rule for the nth term of the sequence

Answer 1

You have the following sequence given in the exercise:

$\frac{1}{4},\frac{2}{4},\frac{3}{4},\frac{4}{4},\ldots$

You can identify that it is an Arithmetic sequence, because the difference between one term and the previous one is always the same:

$\begin{gathered} \frac{2}{4}-\frac{1}{4}=\frac{1}{4} \\ \\ \frac{3}{4}-\frac{2}{4}=\frac{1}{4} \\ \\ \frac{4}{4}-\frac{3}{4}=\frac{1}{4} \end{gathered}$

By definition, you can express an Arithmetic sequence using a rule:

$a_n=a_1+d(n-1)_{}$

Where:

- The nth term of the sequence is

$a_n$

- The first term is

$a_1$

- The common difference is "d".

- The term position is "n".

In this case you know that:

$\begin{gathered} d=\frac{1}{4} \\ \\ a_1=\frac{1}{4} \end{gathered}$

Therefore, you can substitute this value into

$a_n=a_1+d(n-1)_{}$

Then, you get that the answer is:

$a_n=\frac{1}{4}+\frac{1}{4}(n-1)$