Question

write a recursive sequence that represents the sequence defined by the following explicit formula:
$a_n = 10 + 4(n - 1)$
answer attempt 1 out of 3
$a_1 = \square$
$a_n = \square$
submit answer $a_{n - 1}$

Explanation:

Step1: Find \(a_1\)

To find the first term \(a_1\), substitute \(n = 1\) into the explicit formula \(a_n=10 + 4(n - 1)\).

$$
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Step2: Determine the recursive formula

The explicit formula \(a_n = 10+4(n - 1)\) represents an arithmetic sequence with common difference \(d = 4\). For an arithmetic sequence, the recursive formula is \(a_n=a_{n - 1}+d\) (where \(n\geq2\)). Since \(d = 4\), the recursive formula is \(a_n=a_{n - 1}+4\) with \(a_1 = 10\).

Answer:

\(a_1=\boldsymbol{10}\)
\(a_n=\boldsymbol{a_{n - 1}+4}\) (for \(n\geq2\))