Question

Following one side of a rural road, the house numbers increase by eighteen. The house number of the first house on the road is 82. Express this sequence recursively and explicitly.

Answer 1

Answer:

Recursive:

$a_n=a_{(n-1)}+18\\ \\ a_1=82$

Explicit:

$a_n=64+18n$

Explanation:

1. Sequence:

$a_1=82\\ \\ a_2=82+18=100\\ \\ a_3=100+18=118\\ \\ a_4=118+18=136\\ \\ ...$

2. Recursive formula

The recursive formula permits to calculate the value of the nth term in the sequence using the (n-1)th term in the sequence.

$a_n=a_{(n-1)}+18\\ \\ a_1=82$

3. Explicit formula

The explicit formula permits to calculate any value of a term in the sequence:

$a_n=a_1+(n-1)d\\ \\ a_n=82+(n-1)18\\ \\ a_n=82+18n-18\\ \\ a_n=64+18n$