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 11 Page 444

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

a_n=16n-28

Practice makes perfect
The explicit rule of an arithmetic sequence combines the information provided by the two equations of the recursive rule into a single equation. Recursive:& a_n=a_(n-1)+ d; & a_1= a_1 [0.8em] Explicit:& a_n= a_1+(n-1) dIn these rules, d is the common difference and a_1 is the first term. Looking at the given recursive rule, we can identify the common difference d and the value of the first term a_1. a_1= - 12, a_n=a_(n-1)+ 16 We can see that 16 is the common difference and the first term is - 12. Now we have enough information to form an explicit rule for this sequence.
a_n=a_1+(n-1)d
a_n= - 12+(n-1) 16
a_n=- 12+16n-16
a_n=16n-28