Question

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

Answer 1

4) For this sequence, what we have to do is express all the terms with the denominator equal to 6

`\begin{gathered} (1)/(6) \\ (2)/(6)\to(1)/(3) \\ (3)/(6)\to(1)/(2) \\ (4)/(6)\to(2)/(3) \\ (5)/(6) \\ (6)/(6)\to1 \end{gathered}`

Then the 2 values that follow the sequence are:

`(5)/(6)\text{ , 1}`

5) For this sequence we can see that we only have to add the consecutive numbers:

`\begin{gathered} 0+1=1 \\ 1+2=3 \\ 3+3=6 \\ 6+4=10 \\ 10+5=15 \\ 15+6=21 \\ 21+7=28 \\ 28+8=36 \end{gathered}`

Then the 2 values that follow the sequence are:

`28,36`

6) For this sequence we can see that the consecutive numbers are squared:

`\begin{gathered} 1^2\to1 \\ 2^2\to4 \\ 3^2\to9 \\ 4^2\to16 \\ 5^2\to25 \\ 6^2\to36 \\ 7^2\to49 \\ 8^2\to64 \end{gathered}`

Then the 2 values that follow the sequence are:

`49,64`