Big Ideas Math Algebra 2, 2014
BI
Big Ideas Math Algebra 2, 2014 View details
5. Using Recursive Rules with Sequences
Continue to next subchapter

Exercise 35 Page 447

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

a_1=1.9, a_n=a_(n-1)-0.6

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=2.5-0.6n
a_1=2.5-0.6( 1)
a_1=2.5-0.6
a_1=1.9
We know that a_1= 1.9, so now we need to identify the value of d. Let's take a look at the given rule. a_n=2.5-0.6n Notice that the coefficient of n is -0.6, so we know that the terms are decreasing by 0.6 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 -0.6. Now we have enough information to form a recursive rule for our sequence. a_n= & a_(n-1)+( - 0.6); a_1= & 1.9 [0.8em] Therefore, the recursive rule for our sequence is a_1=1.9, a_n=a_(n-1)-0.6.