Chapter 6.7, Problem 35E

To determine

To determine the recursive rule and an explicit rule for the given sequence.

Answer to Problem 35E

Recursive,

  $a_n=a_{n-1}+15$

Explicit,

  $a_n=5+\left(n-1\right)15$

Explanation of Solution

Given information :

The first term of the sequance is 5. Each term of the sequaence is 15 more than the preceding term.

First we shall graph the given sequence.

First term is 5.

Second term is 5+15=20 and so on.

Graph is,

  

Recursive rule is,

  $a_n=a_{n-1}+d$

It is given that $d=15$

Hence we get, $a_n=a_{n-1}+15$

Explicit rule is $a_n=a_1+\left(n-1\right)d$

Put the values we get,

  $a_n=5+\left(n-1\right)15$