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The recursive formula for an arithmetic sequence is:

[tex]
\left\{\begin{array}{l}
a_1 = -9 \\
a_n = a_{n-1} + 3
\end{array}\right.
[/tex]

What is the 3rd term in the sequence?

A. 0
B. -27
C. -3
D. -12

Sagot :

GinnyAnsweridn
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
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