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.
