Question

For Exercises 4−16, use inductive reasoning to find the next two terms in each sequence, insert your sketches for 12, 14, and 16.

Answer 1

Given:

The sequence is,

$\frac{1}{6},\frac{1}{3},\frac{1}{2},\frac{2}{3},\ldots.\ldots\ldots...\ldots$

For the given sequence,

$\begin{gathered} a_0=\frac{1}{6} \\ a_1=\frac{1}{6}+\frac{1}{6}=\frac{1}{3} \\ a_2=\frac{1}{6}+\frac{1}{3}=\frac{1}{2} \\ a_3=\frac{1}{6}+\frac{1}{2}=\frac{2}{3} \\ In\text{ this way the next 2 terms are,} \\ a_4=\frac{1}{6}+\frac{2}{3}=\frac{5}{6} \\ a_5=\frac{1}{6}+\frac{5}{6}=1 \end{gathered}$

Answer: The next two terms of the given sequence is 5/6 , 1 .