Sure, let's find the 14th term of the given sequence: 4, 7, 10, 13, ...
1. First, identify the type of sequence we have. The sequence provided: 4, 7, 10, 13, ... is an arithmetic sequence. In an arithmetic sequence, each term after the first is obtained by adding a constant difference to the preceding term.
2. Determine the first term (a) and the common difference (d):
- First term ([tex]\(a\)[/tex]): 4
- Common difference ([tex]\(d\)[/tex]): 7 - 4 = 3
3. The formula for the nth term ([tex]\(a_n\)[/tex]) of an arithmetic sequence is given by:
[tex]\[
a_n = a + (n - 1) \cdot d
\][/tex]
4. We need to find the 14th term ([tex]\(a_{14}\)[/tex]):
- Here, [tex]\(n = 14\)[/tex]
5. Substitute the known values into the formula:
[tex]\[
a_{14} = 4 + (14 - 1) \cdot 3
\][/tex]
6. Simplify inside the parentheses first:
[tex]\[
a_{14} = 4 + 13 \cdot 3
\][/tex]
7. Perform the multiplication:
[tex]\[
a_{14} = 4 + 39
\][/tex]
8. Finally, add the numbers together:
[tex]\[
a_{14} = 43
\][/tex]
Therefore, the 14th term of the sequence is 43.
So, the correct answer is:
A. 43
