describe a pattern in the numbers 4,6,9,13,18
They are monotonically increasing.
They are increasing a distance of n apart, as in
1st, 2nd, 3rd, 4th, 5th, 6th, ...nth
4, 4+2, 6+3, 9+4, 13+5, 18+6, ...(n-1 term)+n
or
term(1) = 4
term(2) = 6
term(3) = term(1) + term(2) - 1 = 9
term(4) = term(2) + term(3) - 2 = 13
term(5) = term(3) + term(4) - 3 = 18
...
term(n) + term(n-2) + term(n-1) - (n-2)
this is called a recursive formula,
or
term(n) = n(n+1)/2 + 3
Including bobpursley's pattern , there are probably some more
Describe a pattern in the numbers: 4, 6, 9, 13, 18
To describe a pattern in the numbers 4, 6, 9, 13, 18, let's examine the differences between each consecutive number:
6 - 4 = 2
9 - 6 = 3
13 - 9 = 4
18 - 13 = 5
Looking at these differences, we can observe that they are increasing by 1 each time. This suggests that the pattern involves adding consecutive numbers starting from 2. Let's verify this by adding consecutive numbers to the last given number:
18 + 6 = 24
24 + 7 = 31
As we can see, the next number in the pattern would be 31. Therefore, the relationship between the numbers in the sequence is that each subsequent number is obtained by adding the next consecutive number, starting from 2, to the previous number.