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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

6. Recursively Defined Sequences

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Exercise 13 Page 316

Can you find the common ratio and the first term just by looking at the explicit formula?

a_n=4a_(n-1); a_1 = - 2.5

Practice makes perfect

The explicit formula of a geometric sequence combines the information provided by the two equations of the recursive form 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 formulas, r is the common ratio and a_1 is the first term. Looking at the given explicit formula, we can identify the common ratio r and the value of the first term a_1. a_n= -2.5( 4)^(n-1) We can see that 4 is the common ratio and the first term is - 2.5. Now we have enough information to form an explicit formula for this sequence. a_n&= 4a_(n-1); a_1&= - 2.5

Subchapter links

Communicate Your Answer p.313

Monitoring Progress p.315-317

Exercises p.318-320