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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 48 Page 319

The given rule means that after the first term of the sequence, every term f(n) is the product of the previous term f(n-1) and 6.

f(2) = - 6, f(5) = - 1296, f(10) = - 10 077 696

Practice makes perfect

We are asked to write the 2nd, 5th and 10th term of a sequence, given a recursive rule. \begin{aligned} f(1)&=\text{-} 1 \\ f(n)&=6f(n-1), \text{ for } n>1 \end{aligned} Let's use a table.

n f(n)=6f(n-1) f(n)
1 f( 1)=- 1 - 1
2 f( 2)=6f( 2-1)
⇕
f(2)=6 f(1) 		f(2)=6( - 1)
⇕
f(2)= - 6
3 f( 3)=6f( 3-1)
⇕
f(3)=6 f(2) 		f(3)=6( - 6)
⇕
f(3)= - 36
4 f( 4)=6f( 4-1)
⇕
f(4)=6 f(3) 		f(4)=6( - 36)
⇕
f(4)= - 216
5 f( 5)=6f( 5-1)
⇕
f(5)=6 f(4) 		f(5)=6( - 216)
⇕
f(5)= - 1296
6 f( 6)=6f( 6-1)
⇕
f(6)=6 f(5) 		f(6)=6( - 1296)
⇕
f(6) - 7776
7 f( 7)=6f( 7-1)
⇕
f(7)=6 f(6) 		f(7)=6( - 7776)
⇕
f(7)= - 46 656
8 f( 8)=6f( 8-1)
⇕
f(8)=6 f(7) 		f(8)=6( - 46 656)
⇕
f(8)= - 279 936
9 f( 9)=6f( 9-1)
⇕
f(9)=6 f(8) 		f(9)=6( - 279 936)
⇕
f(9)= - 1 679 616
10 f( 10)=6f( 10-1)
⇕
f(10)=6 f(9) 		f(10)=6( - 1 679 616)
⇕
f(10)= - 10 077 696

Therefore, f(2) = - 6, f(5) = - 1296 and f(10) = - 10 077 696.

Subchapter links expand_more
arrow_right Communicate Your Answer p.313
3
Communicate Your Answer 4 (Page 313)
arrow_right Monitoring Progress p.315-317
Monitoring Progress 1 (Page 315)
Monitoring Progress 2 (Page 315)
Monitoring Progress 3 (Page 315)
Monitoring Progress 4 (Page 315)
Monitoring Progress 5 (Page 315)
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Monitoring Progress 14 (Page 317)
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Monitoring Progress 16 (Page 317)
Monitoring Progress 17 (Page 317)
arrow_right Exercises p.318-320
Exercises 1 (Page 318)
Exercises 2 (Page 318)
Exercises 3 (Page 318)
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