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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 26 Page 319

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

a_n = -2(9)^(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 recursive formula, we can identify the common ratio r and the value of the first term a_1. a_1= -2; a_n= 9a_(n-1) We can see that 9 is a common ratio and -2 is the first term. Now we have enough information to form an explicit formula for this sequence. a_n=a_1 * r^(n-1) ⇔ a_n = -2( 9)^(n-1)

Subchapter links

Communicate Your Answer p.313

Monitoring Progress p.315-317

Exercises p.318-320