Input 1 2 4 5 10 12
Output 3 5 9 11 21 25
Write the rule
1 3
2 5
3 try constant difference of 2 -->7
4 9
5 11
6 -->13
7 -->15
8 -->17
9 -->19
10 21
11 --> 23
12 25 so it worked
accordind to my rule
0 1
so
y(n) = 2 + y(n-1)
or y(n) = 1 + 2(n)
y = 2 n + 1
To find the output for each input number, we can follow the following rule:
1. Multiply each input number by 2.
2. Add 1 to the result obtained in step 1.
Therefore, the rule can be written as follows:
Output = (Input * 2) + 1
To find the rule that generates the output sequence, let's analyze how each number in the output is related to the corresponding number in the input sequence.
Looking at the input sequence and the output sequence:
Input: 1 2 4 5 10 12
Output: 3 5 9 11 21 25
We can observe the following pattern:
1) The first number in the output sequence (3) is obtained by adding 2 to the corresponding number in the input sequence (1 + 2 = 3).
2) The second number in the output sequence (5) is obtained by adding 3 to the corresponding number in the input sequence (2 + 3 = 5).
3) The third number in the output sequence (9) is obtained by multiplying the corresponding number in the input sequence by 2 and then subtracting 1 (4 * 2 - 1 = 9).
4) The fourth number in the output sequence (11) is obtained by adding 6 to the corresponding number in the input sequence (5 + 6 = 11).
5) The fifth number in the output sequence (21) is obtained by multiplying the corresponding number in the input sequence by 2 and then adding 1 (10 * 2 + 1 = 21).
6) The sixth number in the output sequence (25) is obtained by adding 13 to the corresponding number in the input sequence (12 + 13 = 25).
Based on this analysis, we can define the rule for generating the output sequence as follows:
- If the index of a number in the input sequence is odd, add the index number itself to the corresponding number in the input sequence.
- If the index of a number in the input sequence is even, multiply the corresponding number in the input sequence by 2 and then add the index number minus 1.
By applying this rule to each number in the input sequence, we can generate the corresponding number in the output sequence.