Q22. - Algebra 1

Question

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

$-40,-32,-24,-16,\mathrm{.....}$

Step-by-Step Solution

Answer

The given sequence is an arithmetic sequence and the common difference is 8.

Step 1. State the concept of arithmetic sequence.

In an Arithmetic Sequence the difference between one term and the next is a constant.

The nth term 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.

$\begin{array}{c}d=a_2-a_1=-32-\left(-40\right)=-32+40=8\\ d=a_3-a_2=-24-\left(-32\right)=-24+32=8\\ d=a_4-a_3=-16-\left(-24\right)=-16+24=8\end{array}$

Step 3. State the Conclusion.

In the above step, the common difference is constant and its value is 8.

 

Hence the given sequence is an arithmetic sequence and its common difference is 8.