Question

An arithmetic sequence has this recursive formula:

Answer 1

Answer:

$a_n = 5 + (n - 1)(-4)$

Step-by-step explanation:

The recursive formula given is:

$\left \{ {a_1 = 5} \atop {a_n = a_{n - 1} - 4} \right.$

Generally a recursive formula is given as:

$\left \{ {a_1 = a} \atop {a_n = a_{n - 1} + d}} \right.$

where a = first term

d = common difference

This implies that:

a = 5

d = -4

A general formula for an arithmetic sequence is:

$a_n = a + (n - 1)d$

Therefore, the general formula for the sequence is:

$a_n = 5 + (n - 1)(-4)$