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 9 Page 444

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

a_1=13, a_n=a_(n-1)-4

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) d In both of these rules, d is the common difference and a_1 is the first term. Let's start by substituting 1 for n in the given rule in order to find the value of a_1.
a_n=17-4n
a_1=17-4( 1)
a_1=17-4
a_1=13
We know that a_1= 13, so now we need to identify the value of d. Let's take a look at the given rule. a_n=17-4n Notice that the coefficient of n is -4, so we know that the terms are decreasing by 4 each time. For the n^(th) term, the number of times it has decreased in relation to a_1 is given by the value of n. Therefore, the common difference d is -4. Now we have enough information to form a recursive rule for our sequence. a_n= & a_(n-1)+( - 4); a_1= & 13 [0.8em] Therefore, the recursive rule for our sequence is a_1=13, a_n=a_(n-1)-4.