Question

(ii) Sequence A: 4; 7; 10; 13: 16;......
Sequence B: 5; 10; 20; 40; 80;.
Sequence C: 2; 5; 10; 17; 26; ..
(a) Write down the next three numbers in each of given sequences.
Sequence A:
(2)
(3)
Sequence B:
Sequence C:
(b) Write down how you decided what the next number would be in each of the thr
sequences.
Sequence A:
E)
Sequence B:
Sequence C:
[1

Answer 1

Sure! Let's analyze each sequence step-by-step to determine the next three numbers and explain how these numbers were determined.

### Sequence A: 4, 7, 10, 13, 16, ...
#### (a) Next three numbers
This sequence is an arithmetic progression (AP) where the difference between consecutive terms is constant.

The common difference $\( d \)$ can be found by subtracting any term from the next term:
$\[ d = 7 - 4 = 3 \]$

To find the next three terms:
1. $\( 16 + 3 = 19 \)$
2. $\( 19 + 3 = 22 \)$
3. $\( 22 + 3 = 25 \)$

So, the next three numbers are:
- 19
- 22
- 25

#### Sequence A:
(1) 19
(2) 22
(3) 25

### Sequence B: 5, 10, 20, 40, 80, ...
#### (a) Next three numbers
This sequence is a geometric progression (GP) where each term after the first is multiplied by a constant ratio.

The common ratio $\( r \)$ can be found by dividing any term by the previous term:
$\[ r = \frac{10}{5} = 2 \]$

To find the next three terms:
1. $\( 80 \times 2 = 160 \)$
2. $\( 160 \times 2 = 320 \)$
3. $\( 320 \times 2 = 640 \)$

So, the next three numbers are:
- 160
- 320
- 640

#### Sequence B:
(1) 160
(2) 320
(3) 640

### Sequence C: 2, 5, 10, 17, 26, ...
#### (a) Next three numbers
This sequence follows a pattern where each term appears to be $\( n^2 + 1 \)$ for $\( n \)$.

For example:
1. $\( 1^2 + 1 = 2 \)$
2. $\( 2^2 + 1 = 5 \)$
3. $\( 3^2 + 1 = 10 \)$
4. $\( 4^2 + 1 = 17 \)$
5. $\( 5^2 + 1 = 26 \)$

To find the next three terms, we continue this pattern for $\( n = 6, 7, 8 \)$:
1. $\( 6^2 + 1 = 37 \)$
2. $\( 7^2 + 1 = 50 \)$
3. $\( 8^2 + 1 = 65 \)$

So, the next three numbers are:
- 37
- 50
- 65

#### Sequence C:
(1) 37
(2) 50
(3) 65

### (b) How the next numbers were determined:

#### Sequence A:
This sequence is an arithmetic progression with a common difference of 3. Each term is obtained by adding 3 to the previous term.

#### Sequence B:
This sequence is a geometric progression with a common ratio of 2. Each term is obtained by multiplying the previous term by 2.

#### Sequence C:
This sequence follows the pattern $\( n^2 + 1 \)$. Each term is calculated by taking the position number, squaring it, and adding 1.

If you have any more questions or need further clarification, feel free to ask!