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 8 Page 447

The given rule means that, after the first term of the sequence, every term a_n is the difference between the square of the previous term a_(n-1) and 10.

a_1=1, a_2=- 9, a_3=71, a_4=5031, a_5=25 310 951, a_6=640 644 240 524 391

Practice makes perfect
We are asked to write the first 6 terms of a sequence, given a recursive rule.

a_1&=1 a_n&=(a_(n-1))^2-10 To do so, we will use a table.

n a_n=(a_(n-1))^2-10 (a_(n-1))^2-10 a_n
1 a_1=1 - 1
2 a_2=(a_(2-1))^2-10 ( a_1)^2-10= 1^2-10 - 9
3 a_3=(a_(3-1))^2-10 ( a_2)^2-10=( - 9)^2-10 71
4 a_4=(a_(4-1))^2-10 ( a_3)^2-10= 71^2-10 5031
5 a_5=(a_(5-1))^2-10 ( a_4)^2-10= 5031^2-10 25 310 951
6 a_6=(a_(6-1))^2-10 ( a_5)^2-10= 25 310 951^2-10 640 644 240 524 391

Therefore, the first 6 terms of the sequence are 1, - 9, 71, 5031, 25 310 951 and 640 644 240 524 391.