5. Using Recursive Rules with Sequences
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a_1=1, a_2=- 9, a_3=71, a_4=5031, a_5=25 310 951, a_6=640 644 240 524 391
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.