Friday, April 16, 2010

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.

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