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

Find The Next Three Terms Of The Arithmetic Sequence 35 710 45 class=

Sagot :

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]

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