Answer
Each term is $\frac{3}{7}$ more than the previous term, meaning add $\frac{3}{7}$ to get the next term.
The next three terms are: $\frac{17}{7}, \frac{20}{7},$ and $\frac{23}{7}$.
Work Step by Step
Each term is $\frac{3}{7}$ more than the previous term, meaning add $\frac{3}{7}$ to get the next term.
We are given the first $4$ terms of this series and are asked for the next three terms, $a_{5}$, $a_{6}$, and $a_{7}$.
To get the $5th$ term, add $\frac{3}{7}$ to the $4th$ term:
$a_{5} = a_{4} + \frac{3}{7}$
Plug in the values as given:
$a_{5} = 2 + \frac{3}{7}$
Convert $2$ to an equivalent fraction with $7$ as its denominator:
$a_{5} = \frac{14}{7} + \frac{3}{7}$
Add:
$a_{5} = \frac{17}{7}$
To get the $6th$ term, add $17$ to the $5th$ term:
$a_{6} = a_{5} + \frac{3}{7}$
Plug in the values as given:
$a_{6} = \frac{17}{7} + \frac{3}{7}$
Add:
$a_{6} = \frac{20}{7}$
To get the $7th$ term, add $17$ to the $6th$ term:
$a_{7} = a_{6} + \frac{3}{7}$
Plug in the values as given:
$a_{7} = \frac{20}{7} + \frac{3}{7}$
Add:
$a_{7} = \frac{23}{7}$
