Question

Determine whether each sequence is an arithmetic sequence. If it is,state the common difference.

$5,17,29,\mathrm{41.....}$

Short answer

The given sequence is an arithmetic sequence and the common difference is 12.

Step-by-step solution

Step 1. State the concept of arithmetic sequence.

In anArithmetic Sequencethe difference between one term and the next is a constant.

The nthterm of the Arithmetic sequence is given by the formula,

$$\begin{gathered} a_n=a+\left(n-1\right)d \\ d=a_2-a_1 \end{gathered}$$

Where,$a_1=a=$ first term and$d=$ common difference.

Step 2. Find the common difference of corresponding terms.

The common difference between the corresponding terms are calculated as follows.

$$\begin{gathered} d=a_2-a_1=17-5=12 \\ d=a_3-a_2=29-17=12 \\ d=a_4-a_3=41-29=12 \end{gathered}$$

Step 3. State the Conclusion.

In the above step, the common difference is constant.

Hence the given sequence is an arithmetic sequence and its common difference is 12.