Question

Find the sum of the consecutive numbers, as shown below:
1) + 2
+
3
+ (4) + (5 + 6
3 x 7 = 21
7
1
+ 2) + (3
+(4+5
6 + 6 + 3 = 15
6
(a) 1 + 2 +3 +4 +5 + 6 + 7 + 8 =​

Answer 1

Answer:

The three consecutive numbers in different patterns are explained here.

(i) The sum of any three consecutive numbers is three times of the middle number:

1 + 2 + 3 = 6 = 3 x 2

2 + 3 + 4 = 9 = 3 x 3

7 + 8 + 9 = 24 = 3 x 8

24 + 25 + 26 = 75 = 3 x 25

37 + 38 + 39 = 114 = 3 x 38

(ii) The sum of any four consecutive numbers is twice the sum of two middle numbers:

1 + 2 + 3 + 4 = 10 = 2 (2 + 3) = 2 x 5

2 + 3 + 4 + 5 = 14 = 2 (3 + 4) = 2 x 7

5 + 6 + 7 + 8 = 26 = 2 (6 + 7) = 2 x 13

17 + 18 + 19 + 20 = 74 = 2 (18 + 19) = 2 x 37

40 + 41 + 42 + 43 = 166 = 2 (41 + 42) = 2 x 83