input 2 ___ ___ 7 15 6
output 11 20 35 26 50 23
please help me solve this.
To solve this problem, you need to understand the pattern and the rules governing the sequence of numbers in the input-output question.
Looking at the input sequence, it seems that there is a pattern associated with converting the input numbers to the output numbers. Let's break it down step by step:
1. The first number in the input sequence is 2. There is no clear indication of what operation or rule is being applied here. However, we can observe that the first number in the output sequence is 11, which is 2 multiplied by 5 and then increased by 1. So, we can assume that this rule applies to every number in the input sequence.
2. The second number in the input sequence is unknown (represented by ___). We need to determine its value. Looking at the second number in the output sequence (20), we can analyze it based on the first rule that we derived. If the second input number is x, then the second output number is obtained by multiplying x by 5 and increasing it by 1. So, we can set up an equation: 5x + 1 = 20. By solving this equation, we find that x = 3. Therefore, the second number in the input sequence is 3.
3. The third number in the input sequence is also unknown. Using the same logic as above, we can set up an equation: 5x + 1 = 35. Solving this equation gives us x = 6. Hence, the third number in the input sequence is 6.
4. Continuing this process for the remaining numbers in the input sequence, we can find the values for the unknown numbers. Following the same equation setup, the fourth number is (5 x 7) + 1 = 36, the fifth number is (5 x 15) + 1 = 76, and the sixth number is (5 x 6) + 1 = 31.
Therefore, the complete input sequence is: 2, 3, 6, 7, 15, 6.
And the corresponding output sequence is: 11, 20, 35, 26, 50, 23.