Chapter 9.1, Problem 4LC

Solution

To determine an explicit formula for the given sequence.

  $a_n=3n+2$

Given:

The given sequence is:

  $5,8,11,14,\dots$

Calculation:

An explicit formula is a formula that describes the $n^{th}$ term of a sequence using the number $n.$ To find the explicit formula, the first step is to identify the pattern between two constative terms and then find the explicit formula.

Now, for the given sequence, the difference between the first two terms is $8-5=3$ .And the difference between third and fourth term is again $14-11=3$ . Hence, for the given sequence, the difference between successive terms is same. So, the term $3n$ is involved in the given sequence.

Now, to find the given sequence, add $2$ to each term of $3n$ to create an explicit formula for given sequence as:

  $a_n=3n+2$

where

  $n=\text{ position of the unknown term}$