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,

`(1)/(6),(1)/(3),(1)/(2),(2)/(3),\ldots.\ldots\ldots...\ldots`

For the given sequence,

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

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