To solve the problem of finding the 3rd term in the given arithmetic sequence, let's analyze the sequence using the provided recursive formula.
1. Identify the First Term:
The first term [tex]\( a_1 \)[/tex] is given as:
[tex]\[
a_1 = -9
\][/tex]
2. Apply the Recursive Formula:
The recursive formula given is:
[tex]\[
a_n = a_{n-1} + 3
\][/tex]
This means that each term in the sequence is obtained by adding 3 to the previous term.
3. Calculate the Terms:
- Second Term [tex]\((a_2)\)[/tex]:
[tex]\[
a_2 = a_1 + 3
\][/tex]
Substitute [tex]\( a_1 = -9 \)[/tex]:
[tex]\[
a_2 = -9 + 3 = -6
\][/tex]
- Third Term [tex]\((a_3)\)[/tex]:
[tex]\[
a_3 = a_2 + 3
\][/tex]
Substitute [tex]\( a_2 = -6 \)[/tex]:
[tex]\[
a_3 = -6 + 3 = -3
\][/tex]
Thus, the 3rd term in the sequence is [tex]\( a_3 = -3 \)[/tex].
Therefore, the correct answer is:
C. -3
