Certainly! Let's examine the given sequence: 2, 5, 8, 11, 14.
Step-by-Step Solution:
1. Identify First Term (a):
- The first term [tex]\(a\)[/tex] of the sequence is given as 2.
2. Determine the Common Difference (d):
- An arithmetic sequence has a constant difference between consecutive terms.
- Calculate the common difference using any two consecutive terms:
[tex]\[
d = 5 - 2 = 3
\][/tex]
3. Formula for the nth Term:
- The general formula for the nth term of an arithmetic sequence is given by:
[tex]\[
a_n = a + (n-1) \cdot d
\][/tex]
4. Substitute the Values for the 6th Term:
- Here, [tex]\(a = 2\)[/tex], [tex]\(d = 3\)[/tex], and [tex]\(n = 6\)[/tex].
[tex]\[
\begin{align*}
a_6 & = 2 + (6-1) \cdot 3 \\
& = 2 + 5 \cdot 3 \\
& = 2 + 15 \\
& = 17
\end{align*}
\][/tex]
Therefore, the 6th term of the sequence is [tex]\(a_6 = 17\)[/tex].
