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Practice each question, then open the answer or worked solution.
Look for the rules and continue these growing patterns:
(a) 51, 56, 61, 66, 71, 76, 81, 86
(b) 7, 14, 21, 28, 35, 42, 49, 56, 63
(c) 2, 4, 8, 16, 32, 64, 128, 256, 512
(d) 12A, 13B, 14C, 15D, 16E, 17F, 18G
Look at these growing patterns. Find out what to add to each number to get the next one:
(a) 1, 3, 6, 10, __, __, __, __, __.
First number: 1
Second number: 3 (i.e., 1 + 2)
Third number: 6 (i.e., 3 + 3)
Fourth number: 10 (i.e., 6 + 4)
Thus, the next number will be
10 + 5 = 15
15 + 6 = 21
21 + 7 = 28
28 + 8 = 36
36 + 9 = 45
So, the final pattern will be: 1, 3, 6, 10, 15, 21, 28, 36, 45.
(b) 0, 2, 6, 12, __, __, __, __, __.
First number: 0
Second number: 2 (i.e., 0 + 2)
Third number: 6 (i.e., 2 + 4)
Fourth number: 12 (i.e., 6 + 6)
Thus, the next number will be
12 + 8 = 20
20 + 10 = 30
30 + 12 = 42
42 + 14 = 56
56 + 16 = 72
So, the final pattern will be: 0, 2, 6, 12, 20, 30, 42, 56, 72.
(c) 1, 3, 7, 13, __, __, __, __, __.
First number: 1
Second number: 3 (i.e., 1 + 2)
Third number: 7 (i.e., 3 + 4)
Fourth number: 13 (i.e., 7 + 6)
Thus, the next number will be
13 + 8 = 21
21 + 10 = 31
31 + 12 = 43
43 + 14 = 57
57 + 16 = 73
So, the final pattern will be: 1, 3, 7, 13, 21, 31, 43, 57, 73.
(d) 2, 3, 6, 11, 18, __, __, __, __, __.
First number: 2
Second number: 3 (i.e., 2 + 1)
Third number: 6 (i.e., 3 + 3)
Fourth number: 11 (i.e., 6 + 5)
Fifth number: 18 (i.e., 11 + 7)
Addition of sequence of odd numbers, i.e. 1, 3, 5, 7 …
Thus, the next number will be
18 + 9 = 27
27 + 11 = 38
38 + 13 = 51
51 + 15 = 66
66 + 17 = 83
So, the final pattern will be: 2, 3, 6, 11, 18, 27, 38, 51, 66, 83.
SECRET MESSAGES
Amrita and Paritosh are writing secret messages.
Question 1:
Can you tell what they are trying to say?
Where are you?
In the canteen.
Question 2:
These are two secret messages. Look for the patterns and find the hidden sentences.
1 I 2 L 3 O 4 V 5 E 6 Y 7 O 8 U
ATBHCIDS EBFOGOHK IIJS KFLUMN
I LOVE YOU
THIS BOOK IS FUN