Question

Write the next two terms of the following sequence $\frac{2}{3},\frac{3}{4},\frac{4}{5},$ _____ , ____

Answer 1

In the given sequence is $\frac{2}{3},\frac{3}{4},\frac{4}{5},......$, the first term $t_1=\frac{2}{3}$, second term $t_2=\frac{3}{4}$ and third term $t_3=\frac{4}{5}$.

We observe that:

$t_1=\frac{1+1}{(1+1)+1}=\frac{2}{3}$ and

$t_2=\frac{2+1}{(2+1)+1}=\frac{3}{4}$ and so on...

Therefore, the next two terms of the sequence is:

$t_4=\frac{4+1}{(4+1)+1}=\frac{5}{6}$ and

$t_5=\frac{5+1}{(5+1)+1}=\frac{6}{7}$

Hence, the next two terms are $\frac{5}{6}$ and $\frac{6}{7}$.