6. Recursively Defined Sequences
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Make a table to organize the terms. Then find the pattern.
a_1=2, a_n=a_(n-1)+1.5
Let's make a table that shows the height of the sunflower for each month.
From the table we see that there is a common difference of 1.5, making it an arithmetic sequence. Since we know d= 1.5, we can use a recursive equation for the arithmetic sequence. a_n=a_(n-1)+ d ⇒ a_n=a_(n-1)+ 1.5 The recursive rule is the recursive equation together with the first term. Recursive Rule: a_1=2, a_n=a_(n-1)+1.5