Answer to Question #161959 in Discrete Mathematics for tanya

Question

1. Blue taxi inc. charges $7.50 for the first 4 miles and 1 dollar for each additional miles. The table shows the cost of travelling from 4 to 10 miles.

Mileage Cost

4. 7.50

5. 8.50

6. 9.50

7. 10.50

8. 11. 50

9. 12.50.

10. 13.50

• Write the recursive formula.
• Write the explicit formula

2. If the sequence formula is given as t_{n =} n² -1, n less than or equal to 1.

• Write the first five terms of the sequence
• Write the 55th term

Answer 1

1.Denote by c_n the cost of travelling for n miles. Then

c_n=c_n-1+1 if n>4 and c_n=c_n-1=7.5 else.

Explicit formula:

c_n=n+3.5 if n>4 and c_n=7.5 else.

2. t_n = n² -1, n less than or equal to 1.

t₁ = 1²-1 = 0

t₂ = 2²-1=3

t₃ = 3²-1=8

t₄ = 4²-1=15

t₅ = 5²-1=24

t₅₅ = 55²-1=3024