Given the number pattern 2,5,10,17
Provide a rule to describe the relationship between the numbers in this number pattern
The rule to describe the relationship between the numbers in this number pattern is that each subsequent number is obtained by adding the next odd number.
Starting with 2:
2 + 1 (the first odd number) = 3
3 + 2 (the second odd number) = 5
5 + 3 (the third odd number) = 8
8 + 4 (the fourth odd number) = 12
12 + 5 (the fifth odd number) = 17
Therefore, the pattern is formed by adding consecutive odd numbers to the previous number.
To find the rule for the number pattern 2, 5, 10, 17, we need to examine the differences between the terms.
The difference between the first and second term is 5 - 2 = 3.
The difference between the second and third term is 10 - 5 = 5.
The difference between the third and fourth term is 17 - 10 = 7.
From these differences, we can see that the differences themselves form a pattern: 3, 5, 7.
To find the next difference, we can add 2 to the previous difference: 7 + 2 = 9.
Using these differences, we can find the subsequent terms:
First term: 2
Second term: 2 + 3 = 5
Third term: 5 + 5 = 10
Fourth term: 10 + 7 = 17
Fifth term: 17 + 9 = 26
Therefore, the rule for this number pattern is to add the increasing sequence of odd numbers (starting from 3) to the previous term.