Question

write an explicit formula that represents the sequence defined by the following recursive formula:
$a_1 = -3$ and $a_n = a_{n-1} + 8$

Explanation:

Step1: Identify Sequence Type

The recursive formula \( a_n = a_{n - 1}+8 \) and \( a_1=-3 \) shows this is an arithmetic sequence, where the first term \( a_1=-3 \) and common difference \( d = 8 \).

Step2: Recall Arithmetic Sequence Formula

The explicit formula for an arithmetic sequence is \( a_n=a_1+(n - 1)d \).

Step3: Substitute Values

Substitute \( a_1=-3 \) and \( d = 8 \) into the formula:

$$
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$$

Answer:

\( a_n = 8n - 11 \)