Question

Find the next three terms of the arithmetic sequence. 3/5, 7/10, 4/5,...

Answer 1

Answer:

$\frac{9}{10},1\text{ and 1}\frac{1}{10}$

Explanation:

Given the arithmetic sequence

$\frac{3}{5},\frac{7}{10},\frac{4}{5}\text{.}\cdots$

We can rewrite all the fractions using a denominator of 10 as follows:

$\begin{gathered} \frac{3\times2}{5\times2},\frac{7}{10},\frac{4\times2}{5\times2},\cdots \\ =\frac{6}{10},\frac{7}{10},\frac{8}{10},\cdots \end{gathered}$

We observe that the denominator remains the same but the numerator increases by 1.

Therefore, the next three terms of the arithmetic sequence are:

$\begin{gathered} \frac{9}{10},\frac{10}{10}\text{ and }\frac{11}{10} \\ =\frac{9}{10},1\text{ and 1}\frac{1}{10} \end{gathered}$