Exercise 50 Page 319

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

f(2) = 5, f(5) = 23, f(10) = 254

Practice makes perfect

We are asked to write the 2nd, 5th and 10th term of a sequence, given a recursive rule and the first two terms. \begin{aligned} f(1)&=4 \\ f(2)&=5 \\ f(n)&=f(n-1)+f(n-2), \text{ for } n>2 \end{aligned} Let's use a table.

n	f(n)=f(n-1)+f(n-2)	f(n)
1	f( 1)=4	4
2	f( 2)=5	5
3	f( 3)=f( 3-1)+f( 3-2) ⇕ f(3)= f(2)+ f(1)	f(3)= 5+ 4 ⇕ f(3)= 9
4	f( 4)=f( 4-1)+f( 4-2) ⇕ f(4)= f(3)+ f(2)	f(4)= 9+ 5 ⇕ f(4)= 14
5	f( 5)=f( 5-1)+f( 5-2) ⇕ f(5)= f(4)+ f(3)	f(5)= 14+ 9 ⇕ f(5)= 23
6	f( 6)=f( 6-1)+f( 6-2) ⇕ f(6)= f(5)+ f(4)	f(6)= 23+ 14 ⇕ f(6)= 37
7	f( 7)=f( 7-1)+f( 7-2) ⇕ f(7)= f(6)+ f(5)	f(7)= 37+ 23 ⇕ f(7)= 60
8	f( 8)=f( 8-1)+f( 8-2) ⇕ f(8)= f(7)+ f(6)	f(8)= 60+ 37 ⇕ f(8)= 97
9	f( 9)=f( 9-1)+f( 9-2) ⇕ f(9)= f(8)+ f(7)	f(9)= 97+ 60 ⇕ f(9)= 157
10	f( 10)=f( 10-1)+f( 10-2) ⇕ f(10)= f(9)+ f(8)	f(10)= 157+ 97 ⇕ f(10)= 254

Therefore, f(2) = 5, f(5) = 23 and f(10) = 254.

Subchapter links

Communicate Your Answer p.313

Monitoring Progress p.315-317

Exercises p.318-320

Exercise 50 Page 319

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