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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 59 Page 320

Look for a pattern in the difference of the consecutive terms.

a_1=3, a_n=a_(n-1)+2^n

Practice makes perfect

We are asked to write a recursive rule for the sequence. 3, 7, 15, 31, 63, ... Let's look for a pattern in the difference of the consecutive terms.

We see that each difference is a power of 2. Consider the difference between the fourth and the third term, 2 and 4. a_4=a_3+2^4 ⇔ a_4=a_(4-1)+2^4 We can write the recursive equation. a_n=a_(n-1)+2^n The first term and the recursive equation gives us the recursive rule. Recursive Rule: a_1=3, a_n=a_(n-1)+2^n

Subchapter links

Communicate Your Answer p.313

Monitoring Progress p.315-317

Exercises p.318-320