To write the explicit formula for the nth term of the arithmetic sequence 11, 15, 19, ..., let's follow these steps:
1. Identify the first term:
- The first term ([tex]\(a_1\)[/tex]) of the sequence is 11.
2. Determine the common difference:
- The common difference ([tex]\(d\)[/tex]) is found by subtracting the first term from the second term.
- [tex]\(d = 15 - 11 = 4\)[/tex].
3. Write the general explicit formula for an arithmetic sequence:
- The general formula for the nth term of an arithmetic sequence is given by:
[tex]\[
a_n = a_1 + (n - 1) \cdot d
\][/tex]
4. Substitute the identified values into the formula:
- Substitute [tex]\(a_1 = 11\)[/tex] and [tex]\(d = 4\)[/tex] into the general formula:
[tex]\[
a_n = 11 + (n - 1) \cdot 4
\][/tex]
By simplifying the formula, we get:
[tex]\[
a_n = 11 + (n - 1) \cdot 4
\][/tex]
Thus, the explicit formula for the nth term of the sequence 11, 15, 19, ... is:
[tex]\[
a_n = 11 + (n - 1) \cdot 4
\][/tex]
