A recursive rule for an arithmetic sequence is $a_{1} = 4$ ; $a_{n} = a_{n - 1} + 3$ .
What is an explicit rule for this sequence?

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Solution

Find the explicit rule for the given sequence :
Formula for finding the $n^{t h}$ term in an AP sequence is given by,
$a_{n} = a + (n - 1) d$
where, $a_{n}$ is the $n^{t h}$ term, $a$ is the first term, $d$ is the common difference and $n$ is the number of terms of the sequence.
A recursive rule for an arithmetic sequence is $a_{1} = 4$ ; $a_{n} = a_{n - 1} + 3$ .
Therefore, the common difference is $3$ and first term is $4$ .
Use A.P formula and write explicit rule as:
$a_{n} = 4 + (n - 1) 3$
Hence, the explicit rule for the given sequence is $a_{n} = 4 + (n - 1) 3$ .

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