Discrete Mathematics An Open Introduction, 4th Edition

Explore the first sequence of dots from the Investigate! activity. We will let $a_n$ represent the number of dots in figure $n\text{.}$ The sequence starts $1,5,9,\dots$

Now look at the second sequence of dots from the Investigate! activity. We will let $a_n$ represent the number of dots in figure $n\text{.}$ The sequence starts $2,6,18,\dots$

Now look at the third sequence of dots from the Investigate! activity. We will let $a_n$ represent the number of dots in figure $n\text{.}$ The sequence starts $1,3,6,10,\dots$