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

$\begin{gathered} \frac{1}{6} \\ \frac{2}{6}\to\frac{1}{3} \\ \frac{3}{6}\to\frac{1}{2} \\ \frac{4}{6}\to\frac{2}{3} \\ \frac{5}{6} \\ \frac{6}{6}\to1 \end{gathered}$

Then the 2 values that follow the sequence are:

$\frac{5}{6}\text{ , 1}$

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:

$49,64$