Suppose you work at a bowling alley. After work one day, you decide to line up bowling pins in a triangular

pattern with one pin in the first row, two pins in the second, three pins in the third, and so on.

(a)

How many total pins would you need to use in order to complete four rows?

(b) How many total pins would you need to use in order to complete ten rows?

(c) How many total pins would you need to use in order to complete one hundred rows?

How about one thousand rows?

1) We are given that every row has one extra pin than the last one and since there are four rows and the First row start with 1 pin then the total number of pins in four rows would be - 1+2+3+4 = 10

2) To complete 10 rows the total number of pins needed would be-

Applying arithmetic progression to find out Sn = n/2 (2a + (n-1) d) = 5 x (2+9) = 55

3) Now for 100 rows applying same formula again Sn = n/2 (2a + (n-1) d) = 50 x (2+99) = 5050

4) Now for 1000 rows applying the formula Sn = n/2 (2a + (n-1) d) = 500x (2+999) = 500500