A sequence starts $-3$, $1$, $5$, $9$, $\dots$  

1. If you wanted to find the $50^{\text{th}}$ term of the sequence, would an explicit equation or a recursive equation be more useful?

   Hint (a):

   Refer to the Math Notes box in Lesson 4.1.3 for equations of sequences.

2. Write an equation that represents the sequence.

   Hint (b):

   Is the sequence arithmetic or geometric?

   Answer (b):

   Arithmetic

   $a_n=-3+4\left(n-1\right)=4n-7$

3. What is the $50^{\text{th}}$ term of the sequence?

   Hint (c):

   Let $n=50$ in your equation from part (b).

4. Write an explicit equation for the sequence $3$, $2\frac{2}{3}$, $2\frac{1}{3}$, $2$, $1\frac{2}{3}$, $\dots$

   Hint (d):

   Is the sequence arithmetic or geometric?

   More Help (d):

   The common difference is:
   $\frac{1}{3}$