The general rule for the sequence 2,3,5,8,12
note that starting with 2, you have added 1,2,3,4
so, what's next?
To find the general rule for the given sequence, we need to identify the pattern or relationship between the terms.
Looking at the sequence: 2, 3, 5, 8, 12
To get from 2 to 3, we add 1.
To get from 3 to 5, we add 2.
To get from 5 to 8, we add 3.
To get from 8 to 12, we add 4.
From the pattern, we can see that the differences between each term are increasing by 1 each time. This is a sign that the sequence is likely an arithmetic sequence with a common difference of 1.
Using this pattern, we can create the following recursive formula:
a_{n} = a_{n-1} + n, where a_{n} is the nth term of the sequence
Starting with the first term (a_{1} = 2), we can apply the recursive formula to find subsequent terms:
a_{2} = a_{1} + 1 = 2 + 1 = 3
a_{3} = a_{2} + 2 = 3 + 2 = 5
a_{4} = a_{3} + 3 = 5 + 3 = 8
a_{5} = a_{4} + 4 = 8 + 4 = 12
Therefore, the general rule for the sequence 2, 3, 5, 8, 12 is a_{n} = a_{n-1} + n.