



 
Hi Lauren, I see this sequence as points on the line. The steps are of length \[\frac{5}{3}  (2) = \frac{5}{3} + \frac{6}{3} = \frac{1}{3}\] and \[\frac{4}{3}  \frac{5}{3} = \frac{4}{3} + \frac{5}{3} = \frac{1}{3}\] and so on. Each step is of length $\large \frac{1}{3}.$ How many steps does it take you to get to 8? \[2 + \mbox{ length of a step } \times \mbox{ number of steps } = 8\] or \[ \frac{1}{3} \times \mbox{ number of steps } = 10.\] Thus the number of steps is 30. At this point you need to be careful. You start at 2 and the first step gets you to the second term, the second step gets you to the third term and so on. Thus the $30^{th}$ step get yo to the $31^{st}$ term. You can use your formula if you prefer it is just that I don't remember formulas well. Penny  


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