Final answer:
By analyzing the numerical pattern with consecutive numbers summing to 7 and the total sum being 20 for 10 numbers, we find that the average of these numbers is 2.
Step-by-step explanation:
The student has presented a numerical pattern problem where we are given that the sum of any three consecutive numbers is 7, and the total sum of all 10 numbers is 20.
We can start by assigning variables to the first three numbers in the sequence, such as a, b, and c, which gives us 3 equations: a + b + c = 7, b + c + a+1 = 7 (since the fourth number in the sequence will be a+1), and a + b + c + a+1 ... + b+7 = 20. The presence of a repeating pattern indicates that some numbers in the sequence are the same.
By solving these equations or applying logical reasoning, we can deduce that each number in the sequence must repeat thrice except for the first three and last three numbers, which will only appear once. Consequently, the average of the numbers can be calculated by dividing the total sum, which is 20, by the total count of numbers, which is 10. This gives us an average of 2.