Question

How do you find the \[{n^{th}}\] term rule for \[1,5,9,13,...\]?

Answer 1

Hint: In the given question, clearly, we have been given an AP. We have been asked to find the position of any term from the start, i.e., the \[{n^{th}}\] term. For doing that, first we are going to write the first term and common difference of the AP. Then we are going to write the formula of \[{a_n}\] and put in the values for this term.

Formula used:
We are going to use the formula of \[{a_n}\], which is:
\[{a_n} = a + \left( {n - 1} \right)d\]

Complete step-by-step answer:
The formula for \[{a_n}\] is:
\[{a_n} = a + \left( {n - 1} \right)d\]
Here, first term, \[a = 1\]
common difference, second term minus first term, \[d = 5 - 1 = 4\]
\[{a_n} = 1 + \left( {n - 1} \right)4\]
Opening the brackets,
\[{a_n} = 1 + 4n - 4 = 4n - 3\]
Therefore, the rule for \[{n^{th}}\] term for this AP is “\[4n - 3\]”.

Note: In the given question, we were given an arithmetic progression. We had to write the formula of the \[{n^{th}}\] term. To do that, we write the formula of \[{n^{th}}\]term, put in the values and simplify the answer. We only need to pay attention to the formula of the \[{n^{th}}\]term. It is the only thing around which the answer revolves.