Question

alg : cc unit 1 lt3 7 the recursive formula of an arithmetic sequence is described below. ( a_1 = 13 ), ( a_n = a_{n - 1} + 5 ) which represents the explicit equation of this arithmetic sequence? a ( a_n = 8n + 5 ) b ( a_n = 13n + 5 ) c ( a_n = 5n + 8 ) d ( a_n = 5n + 13 )

Explanation:

Step1: Recall arithmetic sequence formula

The explicit formula for an arithmetic sequence is \( a_n = a_1 + (n - 1)d \), where \( a_1 \) is the first term and \( d \) is the common difference.
Given \( a_1 = 13 \) and the recursive formula \( a_n = a_{n - 1}+5 \), so \( d = 5 \).

Step2: Substitute into the formula

Substitute \( a_1 = 13 \) and \( d = 5 \) into \( a_n = a_1+(n - 1)d \):

$$
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$$

Answer:

C. \( a_n = 5n + 8 \)