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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 33 Page 319

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

a_1 = 1, a_n=- 5a_(n-1)

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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_1= a_1; a_n= r* a_(n-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=( - 5)^(n-1) We can see that - 5 is the common ratio and the first term is 1. Now we have enough information to form a recursive formula for this sequence. la_1 = a_1 a_n = r* a_(n-1) ⇒ la_1 = 1 a_n = - 5a_(n-1)

Subchapter links

Communicate Your Answer p.313

Monitoring Progress p.315-317

Exercises p.318-320