Question

An arithmetic sequence has this recursive formula:

Answer 1

An arithmetic sequence can be expressed as explicitly or recursively

The explicit formula of the sequence is $a_n = 11 - 4n$

How to determine the explicit formula

The recursive formula is given as:

$a_n = a_{n -1} - 4$

$a_1 = 7$

Substitute 2 for n in $a_n = a_{n -1} - 4$

$a_2 =a_1 - 4$

This gives

$a_2 =7 - 4$

$a_2 =3$

Calculate the common difference (d)

$d = a_2 -a_1$

$d = 3- 7$

$d = -4$

The explicit formula is then calculated as:

$a_n = a_1 + (n - 1)d$

This gives

$a_n = 7+ (n - 1)*-4$

Expand

$a_n = 7+4 - 4n$

$a_n = 11 - 4n$

Hence, the explicit formula of the sequence is $a_n = 11 - 4n$

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