How many pins?

In bowling one often uses ten pins positioned on four rows. How many pins are needed for five rows, six rows, or n rows (where n is a positive integer)?

The below procedure calculates the number of pins needed for n rows recurssively.

(define (number-of-pins-rec n)(if(= n 1) n (+ n (number-of-pins-rec(- n 1)))))

> (number-of-pins-rec 2)

3

> (number-of-pins-rec 4)

10

> (number-of-pins-rec 5)

15

> (number-of-pins-rec 6)

21

The procedure in a iterative process.

(define (number-of-pins-it-help n sum count)

(if (> count n)

sum

(number-of-pins-it-help n

(+ sum count)

(+ count 1))))

(define (number-of-pins-it n)

(number-of-pins-it-help n 0 1))

> (number-of-pins-it 3)

6

> (number-of-pins-it 4)

10

> (number-of-pins-it 5)

15

> (number-of-pins-it 6)

21

> (number-of-pins-it 7)

28