Question

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

Answer 1

`(9)/(10),1\text{ and 1}(1)/(10)`

Step-by-step explanation:

Given the arithmetic sequence

`(3)/(5),(7)/(10),(4)/(5)\text{.}\cdots`

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

`\begin{gathered} (3*2)/(5*2),(7)/(10),(4*2)/(5*2),\cdots \\ =(6)/(10),(7)/(10),(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} (9)/(10),(10)/(10)\text{ and }(11)/(10) \\ =(9)/(10),1\text{ and 1}(1)/(10) \end{gathered}`