Question

find the common difference and the next three terms of each arithmetic sequence.

1. $\frac{1}{4},\frac{1}{2},\frac{3}{4},1,\frac{5}{4},ldots$
2. 6, 1, - 4, - 9, - 14, ...
3. 215, 227, 239, 251, ...
4. - 4, - 5, - 6, - 7, ...
5. 4.1, 6.3, 8.5, 10.7, ...
6. - 17, - 9, - 1, 7, 15, ...

Explanation:

5.

Step1: Find common - difference

Subtract the first term from the second term. $d=\frac{1}{2}-\frac{1}{4}=\frac{2 - 1}{4}=\frac{1}{4}$

Step2: Find the next three terms

The next term after $\frac{5}{4}$ is $\frac{5}{4}+\frac{1}{4}=\frac{5 + 1}{4}=\frac{6}{4}=\frac{3}{2}$
The term after $\frac{3}{2}$ is $\frac{3}{2}+\frac{1}{4}=\frac{6+1}{4}=\frac{7}{4}$
The term after $\frac{7}{4}$ is $\frac{7}{4}+\frac{1}{4}=\frac{7 + 1}{4}=2$

Step1: Find common - difference

Subtract the second term from the first term. $d=1 - 6=-5$

Step2: Find the next three terms

The next term after $-14$ is $-14+( - 5)=-19$
The term after $-19$ is $-19+( - 5)=-24$
The term after $-24$ is $-24+( - 5)=-29$

Step1: Find common - difference

Subtract the first term from the second term. $d=227 - 215 = 12$

Step2: Find the next three terms

The next term after $251$ is $251+12 = 263$
The term after $263$ is $263+12 = 275$
The term after $275$ is $275+12 = 287$

Answer:

Common difference: $\frac{1}{4}$; Next three terms: $\frac{3}{2},\frac{7}{4},2$

6.