Question

Write a short description of the pattern in this sequence of six numbers and then follow that pattern to write the next three numbers in the sequence 1/5 2/8 3/11 4/14 5/17 6/20

Answer 1

Answer: The next three terms are $\dfrac{7}{23},\dfrac{8}{26},\dfrac{9}{29}$

Step-by-step explanation:

Since we have given that

$\dfrac{1}{5},\dfrac{2}{8},\dfrac{3}{11},\dfrac{4}{14},\dfrac{5}{17},\dfrac{6}{20}$

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 $\dfrac{n}{3n+2}$

So, the next three terms would be

$\dfrac{7}{3\times 7+2}=\dfrac{7}{23}\\\\\dfrac{8}{3\times 8+2}=\dfrac{8}{26}\\\\\dfrac{9}{3\times 9+2}=\dfrac{9}{29}$

Hence, the next three terms are

$\dfrac{7}{23},\dfrac{8}{26},\dfrac{9}{29}$