Look at the following pattern: 5, 8, 11, 14 ...
Find the general term
To find the general term of the given pattern, we need to observe the common difference between the consecutive terms.
By examining the pattern, we can see that each consecutive term is obtained by adding 3 to the previous term.
Therefore, the common difference is 3.
Using this information, we can write the general term (nth term) of the pattern using the formula for an arithmetic sequence:
nth term = first term + (n - 1) * common difference
In this case, the first term (a1) is 5 and the common difference (d) is 3.
So, the general term of the given pattern is:
nth term = 5 + (n - 1) * 3
Simplifying the equation:
nth term = 5 + 3n - 3
Finally, we have:
nth term = 3n + 2
Therefore, the general term of the given pattern is 3n + 2.
To find the general term of a pattern, we need to look for a relationship between the given terms. In this pattern, we can observe that each term is obtained by adding 3 to the previous term.
To express this relationship algebraically, let's say that the first term of the pattern (5) corresponds to the term number 1 (n = 1). We can then create a formula by starting with the first term and adding 3 multiplied by (n - 1), where n represents the position of the term in the pattern.
So, the general term (Tn) for this pattern can be calculated using the formula:
Tn = 5 + 3(n - 1)
In this case, since the pattern starts with 5 (when n = 1), the formula becomes:
Tn = 5 + 3(n - 1)
Tn = 5 + 3n - 3
Tn = 3n + 2
Therefore, the general term for this pattern is 3n + 2.