State the rule for this pattern:
1,5,11,19
What about: subtract the last number and add 2 to the next term
using your rule, do you get the given sequence?
Here's a method of attack:
You know that 1+3+5+...+n = n^2
adding up the 1st n odd numbers gives you n^2.
In your sequence, you have
1 1+4 1+4+6 1+4+6+8
which looks very similar. So, expect something with n^2 in it.
1 = 2^2-3
5 = 3^2-4
11 = 4^2-5
19 = 5^2-6
So, it looks to me like
Tn = (n+1)^2 - (n+2) = n^2+n-1
To identify the pattern in the given sequence 1, 5, 11, 19, we can follow the rule stated, which is "subtract the last number and add 2 to the next term."
Let's break down the pattern step by step:
Starting with the first term:
1
To get the second term, we subtract the last number (1) and add 2:
1 - 1 + 2 = 2
To get the third term, we subtract the last number (2) and add 2:
2 - 2 + 2 = 2
To get the fourth term, we subtract the last number (2) and add 2:
2 - 2 + 2 = 2
Therefore, the pattern in this sequence does not follow the rule stated. The pattern appears to be:
1, 4, 7, 10, and so on, where each term is obtained by adding 3 to the previous term.