State the rule for this pattern:
1,5,11,19
I want to make sure this is correct add the last number from before and 2 more
Right.
What about subtract the last number and add 2 to the next term
1 = 2 - 1 = 1x2 - 1
5 = 6 - 1 = 2x3 - 1
11 = 12 - 1 = 3x4 - 1
19 = 20-1 = 4x5 - 1
mmmmhhh?
term(n) = n(n+1) - 1
With this pattern, I can jump to any term I want to
e.g. term(23) = 23(24) - 1 = 551
with your method, called a recursive method, you would have to know the term(22) to find
term(23)
To find the rule for the given pattern 1, 5, 11, 19, you should examine the differences between consecutive terms.
First, find the difference between the second term and the first term: 5 - 1 = 4.
Next, find the difference between the third term and the second term: 11 - 5 = 6.
Then, find the difference between the fourth term and the third term: 19 - 11 = 8.
By examining the differences, you can observe that the pattern of differences is increasing by 2 each time. As a result, you can conclude that the rule for this pattern is to add the last number from before and 2 more each time.