The next three terms are: 1/6 , 0 and -1/6
Step-by-step explanation:
Given sequence is:
[tex]\frac{5}{6} , \frac{2}{3} ,\frac{1}{2}, \frac{1}{3} ...[/tex]
First of all, we have to find the common difference
[tex]here\\a_1 = \frac{5}{6}\\a_2 = \frac{2}{3}\\a_3 = \frac{1}{2}\\a_4 = \frac{1}{3}\\d = a_2-a_1 = \frac{2}{3} -\frac{5}{6} = \frac{4-5}{6} = -\frac{1}{6}\\d = a_3 - a_2 = \frac{1}{2} - \frac{2}{3} = \frac{3-4}{6} = =\frac{1}{6}[/tex]
The common difference is -1/6
We can simply add -1/6 to the previous term to find the next terms so,
Adding -1/6 to 1/3
[tex]\frac{1}{3} - \frac{1}{6} = \frac{2-1}{6} = \frac{1}{6}\\\frac{1}{6} - \frac{1}{6} = 0\\0-\frac{1}{6} = -\frac{1}{6}[/tex]
Hence,
The next three terms are: 1/6 , 0 and -1/6
Keywords: Arithmetic sequence, common difference
Learn more about arithmetic sequence at:
- brainly.com/question/2495851
- brainly.com/question/2491745
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