Question

How to tell if a sequence is linear, exponential, quadratic or absolute value as simply as possible without graphing (8th grade algebra) examples will be greatly appreciated

Answer 1

We will have the following:

We will be able to tel apart sequences as follows:

Linear sequence: We have that linear sequences follow the form:

`y=mx+b`

Here "x" represents the iteration value for the sequence, "m" the ratio (slope) and "b" a value that modifies the "position" of the sequence. This sequences grows in a linear manner.

Example:

`\begin{cases}y_{}=2x+2 \\ \\ y_1=4 \\ y_2=6 \\ y_3=8 \\ \ldots\end{cases}`

Exponential sequence: We have that exponential sequences follow the form:

`y=a_1(r)^(x-1)`

Here "a1" is the first term of the sequence, "r" is the ratio and "x" the iteration of the sequence.

We obtain the ratio as follows:

`r=(y_n)/(y_(n-1))`

Example:

`\begin{cases}y=1(5)^(x-1)_{} \\ \\ y_1=1 \\ y_2=5 \\ y_3=25 \\ \\ \ldots\end{cases}`

The ratio for this case:

`r=(y_3)/(y_2)\Rightarrow r=(25)/(5)\Rightarrow r=5`

Quadratic sequence: A quadratic sequence follows the general form