Big Ideas Math Algebra 2, 2014
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Big Ideas Math Algebra 2, 2014 View details
5. Using Recursive Rules with Sequences
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Exercise 33 Page 447

Is it possible to find the common ratio and the first term just by looking at the explicit rule?

a_1=12, a_n=11a_(n-1)

Practice makes perfect
The explicit rule of a geometric sequence combines the information provided by the two equations of the recursive rule into a single equation. Recursive:& a_n= r* a_(n-1); a_1= a_1 Explicit:& a_n= a_1 r^(n-1)

In these rules, r is the common ratio and a_1 is the first term. Looking at the given explicit rule, we can identify the common ratio r and the value of the first term a_1. a_n= 12( 11)^(n-1) We can see that 11 is the common ratio and the first term is 12. Now we have enough information to form a recursive rule for this sequence. a_n=& 11a_(n-1); a_1=& 12