Question

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

$0.75,1.5,3,6,12,\mathrm{.....}$

Short answer

The given sequence is not an arithmetic sequence.

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.

$$\begin{gathered} d=a_2-a_1=1.5-0.75=0.75 \\ d=a_3-a_2=3-1.5=1.5 \\ d=a_4-a_3=6-3=3 \\ d=a_5-a_4=12-6=6 \end{gathered}$$

Step 3. State the conclusion.

Note that the common difference of each corresponding terms are different.

Thus, the given sequence is not an arithmetic sequence.