Answer:
The common difference of the arithmetic sequence is [tex]\boxed{\frac{1}{2}}[/tex].
Step-by-step explanation:
Given:
- [tex]a_1=1[/tex]
- [tex]a_2=\frac{6}{4}[/tex]
- [tex]a_3=2[/tex]
- [tex]a_4=\frac{10}{4}[/tex]
- [tex]a_5=3[/tex]
Find:
Formula:
- [tex]d=a_2-a_1[/tex]
- [tex]d=a_3-a_2[/tex]
- [tex]d=a_4-a_3[/tex]
- [tex]d=a_5-a_4[/tex]
Solution:
- [tex]d=a_2-a_1=\frac{6}{4}-1=\frac{6}{4}-\frac{4}{4}=\frac{2}{4}=\boxed{\frac{1}{2}}[/tex]
- [tex]d=a_3-a_2=2-\frac{6}{4}=\frac{8}{4}-\frac{6}{4}=\frac{2}{4}=\boxed{\frac{1}{2}}[/tex]
- [tex]d=a_4-a_3=\frac{10}{4}-2=\frac{10}{4}-\frac{8}{4}=\frac{2}{4}=\boxed{\frac{1}{2}}[/tex]
- [tex]d=a_5-a_4=3-\frac{10}{4}=\frac{12}{4}-\frac{10}{4}=\frac{2}{4}-\boxed{\frac{1}{2}}[/tex]
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