Find the general term of the set. {8, 12, 16, 20, 24, . . .}
8n
4n + 4
3n + 5
5n + 3
To find the general term of the set {8, 12, 16, 20, 24, . . .}, we need to determine the pattern in the set and express it using a formula.
Looking at the set, you can observe that each term is 4 greater than the previous term. So, we can express the pattern as an arithmetic sequence.
To find the general term, we can use the formula for the nth term of an arithmetic sequence, which is given by:
nth term = a + (n-1)d
Here, 'a' represents the first term of the sequence, 'n' represents the position of the term, and 'd' represents the common difference between consecutive terms.
In our case, the first term 'a' is 8, and the common difference 'd' is 4.
Using the formula, we can substitute these values and get:
nth term = 8 + (n-1)4
Simplifying further:
nth term = 8 + 4n - 4
This can be further simplified to:
nth term = 4n + 4
Therefore, the general term of the set {8, 12, 16, 20, 24, . . .} is 4n + 4.