Answer: The next three terms are [tex]\dfrac{7}{23},\dfrac{8}{26},\dfrac{9}{29}[/tex]
Step-by-step explanation:
Since we have given that
[tex]\dfrac{1}{5},\dfrac{2}{8},\dfrac{3}{11},\dfrac{4}{14},\dfrac{5}{17},\dfrac{6}{20}[/tex]
After analyzing the above pattern, we get that
In numerator , numbers are run in consecutive manner.
In denominator, number is added to 3 to get the next term.
So, the general form would be [tex]\dfrac{n}{3n+2}[/tex]
So, the next three terms would be
[tex]\dfrac{7}{3\times 7+2}=\dfrac{7}{23}\\\\\dfrac{8}{3\times 8+2}=\dfrac{8}{26}\\\\\dfrac{9}{3\times 9+2}=\dfrac{9}{29}[/tex]
Hence, the next three terms are
[tex]\dfrac{7}{23},\dfrac{8}{26},\dfrac{9}{29}[/tex]
