Question

Im confused on how to do these.Solve question 1 and 2

Answer 1

1. The sequence is an arithmetic sequence since there's a common difference of 200 between the terms of the sequence.

2. The sequence is a geometric sequence since there's a common ratio of 4 between the terms of the sequence

Step-by-step explanation:

In an arithmetic sequence, there will be a common difference(d) between the terms of the sequence.

While in a geometric sequence, there will be a common ratio between the terms of the sequence.

1) Given the below sequence;

`-38,162,362,562,762`

Let's determine if the sequence above is an arithmetic or geometric sequence;

`\begin{gathered} 162-(-38)=200 \\ 362-162=200 \\ 562-362=200 \\ 762-562=200 \\ \therefore common\text{ difference(d) = 200} \end{gathered}`

Since there's a common difference of 200 between the terms of the sequence, therefore, we can say that the sequence is an arithmetic sequence.

2) Given the below sequence;

`2,8,32,128,512`

Let's determine if the sequence above is an arithmetic or geometric sequence;

`\begin{gathered} (8)/(2)=4 \\ (32)/(8)=4 \\ (128)/(32)=4 \\ (512)/(128)=4 \\ \therefore common\text{ ratio(r) = 4} \end{gathered}`

Since there's a common ratio of 4 between the terms of the sequence, therefore, we can say that the sequence is a geometric sequence.