Question

What type of sequence and how to write the explicit rule.

Answer 1

The Solution:

Given the sequence below:

`26,18,10,2,\ldots`

We are required to identify the type of sequence and to find the explicit rule for the given sequence.

Step 1:

To determine the type of sequence, we shall run the following check:

`\begin{gathered} a_2-a_1=a_3-a_2\text{ then it is an Arithmetic sequence} \\ \text{ but if} \\ (a_2)/(a_1)=(a_3)/(a_2)\text{ then it is a Geometric sequence.} \end{gathered}`

So,

`\begin{gathered} 18-26=10-18 \\ -8=-8 \\ \text{ Then it follows that the sequence is an Arithmetic sequence.} \end{gathered}`

Thus, the sequence is an arithmetic sequence.

Step 2:

To find the explicit rule, we shall use the formula below:

`a_n=a_1+(n-1)d`

In this case,

`\begin{gathered} a_1=\text{ first term=26} \\ n=\text{ number of terms=?} \\ d=\text{ co}mmon\text{ difference=18-26=-8} \end{gathered}`

Substituting these values in the formula, we get

`\begin{gathered} a_n=26+(n-1)(-8) \\ a_n=26-8(n-1) \end{gathered}`

Therefore, the explicit rule of the sequence is :

`a_n=26-8(n-1)`