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Big Ideas Math Integrated I, 2016 View details

6. Recursively Defined Sequences

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Exercise 55 Page 320

The given rule means that after the first term of the sequence, every term a_n is the sum of 3 times the previous term a_(n-1) and 4.

Terms: 5, 19, 61, 187, and 565
Sequence: Neither
Explanation: See solution.

Practice makes perfect

We are asked to write the first 5 terms of a sequence, given a recursive rule. a_1&=5 a_n&=3a_(n-1)+4 To do so, we will use a table.

n	a_n=3a_(n-1)+4	3a_(n-1)+4	a_n
1	a_1=5	-	5
2	a_2=3(a_(2-1))+4	3( a_1)+4=3( 5)+4	19
3	a_3=3(a_(3-1))+4	3( a_2)+4=3( 19)+4	61
4	a_4=3(a_(4-1))+4	3(a_3)+4=3(61)+4	187
5	a_5=3(a_(5-1))+4	3(a_4)+4=3(187)+4	565

Therefore, the first 5 terms of the sequence are 5, 19, 61, 187, and 565. Let's check if the sequence has a common difference.

There is no common difference, meaning the sequence is not an arithmetic sequence. Let's check for a common ratio.

There is no common ratio, meaning it is not a geometric sequence. As a result, the sequence is neither arithmetic nor geometric.

Subchapter links

Communicate Your Answer p.313

Monitoring Progress p.315-317

Exercises p.318-320

Exercise 55 Page 320

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