Answer :
Let's look at each sequence one by one to find the next three numbers and understand the pattern.
a) Sequence A: 2; 5; 8; 11; 14; 17; 20; 23
The pattern here is that each number increases by 3. Starting from 23:
- 23 + 3 = 26
- 26 + 3 = 29
- 29 + 3 = 32
So, the next three numbers are: 26, 29, 32.
b) Sequence B: 4; 5; 8; 13; 20; 29; 40
Let's calculate the differences between consecutive numbers to find the pattern:
- 5 - 4 = 1
- 8 - 5 = 3
- 13 - 8 = 5
- 20 - 13 = 7
- 29 - 20 = 9
- 40 - 29 = 11
The differences (1, 3, 5, 7, 9, 11) form an increasing sequence of odd numbers, adding 2 each time. The next differences will be 13, 15, and 17:
- 40 + 13 = 53
- 53 + 15 = 68
- 68 + 17 = 85
So, the next three numbers are: 53, 68, 85.
c) Sequence C: 1; 2; 4; 8; 16; 32; 64
In this sequence, each number is obtained by multiplying the previous number by 2:
- 64 \times 2 = 128
- 128 \times 2 = 256
- 256 \times 2 = 512
So, the next three numbers are: 128, 256, 512.
d) Sequence D: 3; 5; 7; 9; 11; 13; 15; 17; 19
Each number in this sequence increases by 2:
- 19 + 2 = 21
- 21 + 2 = 23
- 23 + 2 = 25
So, the next three numbers are: 21, 23, 25.
e) Sequence E: 4; 5; 7; 10; 14; 19; 25; 32; 40
The differences are:
- 5 - 4 = 1
- 7 - 5 = 2
- 10 - 7 = 3
- 14 - 10 = 4
- 19 - 14 = 5
- 25 - 19 = 6
- 32 - 25 = 7
- 40 - 32 = 8
The differences are consecutive whole numbers increasing by 1. So, the next differences will be 9, 10, and 11:
- 40 + 9 = 49
- 49 + 10 = 59
- 59 + 11 = 70
So, the next three numbers are: 49, 59, 70.
f) Sequence F: 2; 6; 18; 54; 162; 486
In this sequence, each number is obtained by multiplying the previous number by 3:
- 486 \times 3 = 1458
- 1458 \times 3 = 4374
- 4374 \times 3 = 13122
So, the next three numbers are: 1458, 4374, 13122.
g) Sequence G: 1; 5; 9; 13; 17; 21; 25; 29; 33
Every number in this sequence increases by 4:
- 33 + 4 = 37
- 37 + 4 = 41
- 41 + 4 = 45
So, the next three numbers are: 37, 41, 45.
