Answer:
[tex]\frac{9}{10},1\text{ and 1}\frac{1}{10}[/tex]
Explanation:
Given the arithmetic sequence
[tex]\frac{3}{5},\frac{7}{10},\frac{4}{5}\text{.}\cdots[/tex]
We can rewrite all the fractions using a denominator of 10 as follows:
[tex]\begin{gathered} \frac{3\times2}{5\times2},\frac{7}{10},\frac{4\times2}{5\times2},\cdots \\ =\frac{6}{10},\frac{7}{10},\frac{8}{10},\cdots \end{gathered}[/tex]
We observe that the denominator remains the same but the numerator increases by 1.
Therefore, the next three terms of the arithmetic sequence are:
[tex]\begin{gathered} \frac{9}{10},\frac{10}{10}\text{ and }\frac{11}{10} \\ =\frac{9}{10},1\text{ and 1}\frac{1}{10} \end{gathered}[/tex]
