Challenging P5 2009 SA1 P2 CHIJ Q16

16. Look at the pattern below.

a) At what position does the number 12 first appear? [3]

b) What is the sum of the first 32 numbers? [2]

1st group -- > 1 , 2 , 3

2nd group -- > 2 , 3 , 4

3rd group -- > 3 , 4 , 5

….

10th group -- > 10 , 11 , 12

10 x 3 = 30 -- > 30th position

a) The number 12 first appears at the 30th position.

1, 2, 3, … 10

(1 + 10) x 10 ÷ 2 = 55

2, 3, 4, … 11

(2 + 11) x 10 ÷ 2 = 65

3, 4, 5, .. 12

(3 + 12) x 10 ÷ 2 = 75

55 + 65 + 75 + 11 + 12 = 218

or

3, 4, 5, … 10

(3 + 10) x 8 ÷ 2 = 52

(1 + 2 + 2 + 3 x 52 + 11 + 11 + 12) + (11 + 12) = 218

b) The sum of the first 32 numbers is 218.