6. Recursively Defined Sequences
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Use a table to organize the terms and find the pattern.
a_1=35, a_n=a_(n-1)-11
Let's look at the given graph. The points represent terms of the sequence.
To write a recursive rule for the given sequence, we will use a table to organize the terms and find the pattern. Let's put in the table coordinates of the points from the graph.
The sequence is arithmetic with first term a_1=35 and common difference d=- 11. To write the recursive rule, we will substitute these values into the general formula for the recursive rule of an arithmetic sequence. la_1=a a_n=a_(n-1)+d ⇒ la_1= 35 a_n=a_(n-1) - 11