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Consider a population that grows according to the recursive rule P sub n equals P sub n minus one plus 120 with initial population P sub zero equals 20. We should recognize this recursive formula as linear growth with a common difference, d, is equal to 120. We first want to find P sub one. When finding P sub one, notice n is equal to one here as well as here. So P sub one is equal to P sub one minus one. Thatd be P sub zero plus 120. But were given P sub zero equals 20, so P sub one is equal to 20 plus 120 which is equal to 140. We find P sub two, n is now equal to two. So, P sub two is equal to P sub two minus one or P sub one plus 120. We just found P sub one. P sub one equals 140. So we have 140 plus 120 which equals 260. Now were asked to find the explicit equation from the recursive equation. We have both the recursive and explicit equations for linear growth given here. Again, where d is the common difference, and P sub zero is the initial value which we know is 20. So we ha
