Inductive reasoning is the process of finding patterns in specific observations and writing a conclusion or conjecture. Since the conjecture is based on observations, it might be false. For example, suppose an observer notices that all the birds around them are white. The observer might inductively reason that all birds in the world are white, which is not true. Inductive reasoning is a practical method used in geometry and algebra for recognizing visual and numerical patterns. For instance, use the first three figures in the following diagram to guess the shape and the number of cubes in the fourth figure. After observing the first three figures, it is reasonable to conclude that the number of cubes increases by $3$ from one figure to the next — one on the top, one on the front, and one on the right. Since the figure starts with $1$ cube and each step adds $3$ cubes, an expression can be written to model the number of cubes in each figure. Here, $n$ represents the number of steps after Figure $1.$ For example, Figure $2$ is one step after Figure $1,$ so $n=1.$ This expression allows the calculation of the number of cubes in any figure of the pattern.

	$n$	Number of Cubes
Figure $1$	$0$	$1+3\cdot 0=1$
Figure $2$	$1$	$1+3\cdot 1=4$
Figure $3$	$2$	$1+3\cdot 2=7$
Figure $4$	$3$	$1+3\cdot 3=10$
Figure $121$	$120$	$1+3\cdot 120=361$