Question

Given the following sequence of numbers find the recursive formula, and the appropriate sequence formula,(arithmetic or geometric) and find the next three numbers in the sequence.5, 9, 13, 17, 21,

Answer 1

We can say that it's an arithmetic sequence since it has a common rate of change or common difference of 4.

Arithmetic sequences are represented by the following formula:

Recursive formula:

$\begin{gathered} a_n=a_{n-1}+d \\ \text{Explicit formula:} \\ a_n=a_1+(n-1)d \\ \text{The next three numbers would be: }a_6,a_7,a_8 \end{gathered}$

an= nth term

a1= 1st term

n= number of terms

d= common difference

$\begin{gathered} a_6=5+(6-1)\cdot4 \\ a_6=25 \\ a_7=5+(7-1)\cdot4 \\ a_7=29_{} \\ a_8=5+(8-1)\cdot4_{} \\ a_8=33 \end{gathered}$