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Big Ideas Math Algebra 2, 2014
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Big Ideas Math Algebra 2, 2014 View details
5. Using Recursive Rules with Sequences
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Exercise 9 Page 447

The given rule means that, after the second term of the sequence, every term f(n) is the difference between the two previous terms f(n-1) and f(n-2).

f(0)=2, f(1)=4, f(2)=2, f(3)=- 2, f(4)=- 4, f(5)=- 2

Practice makes perfect

We are asked to write the first 6 terms of a sequence, given a recursive rule. f(0)&=2, f(1)=4 f(n)&=f(n-1) - f(n-2) To do so, we will use a table.

n f(n)=f(n-1)-f(n-2) f(n-1)-f(n-2) f(n)
0 f( 0)=2 - 2
1 f( 1)=4 - 4
2 f( 2)=f( 2-1)-f( 2-2) f(1)- f(0)= 4- 2 2
3 f( 3)=f( 3-1)-f( 3-2) f(2) - f(1)= 2- 4 - 2
4 f( 4)=f( 4-1) - f( 4-2) f(3)- f(2) = - 2- 2 - 4
5 f( 5)=f( 5-1) - f( 5-2) f(4)- f(3) = - 4- ( - 2) - 2

Therefore, the first 6 terms of the sequence are 2, 4, 2, - 2, - 4 and - 2.

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arrow_right Communicate Your Answer p.441
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arrow_right Monitoring Progress p.442-446
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