To find the nth term of the sequence given (1, 4, 7, 10), we need to identify the pattern or rule that describes the relationship between the terms in the sequence.
Looking at the sequence, we see:
- The first term (n=1) is 1
- The second term (n=2) is 4
- The third term (n=3) is 7
- The fourth term (n=4) is 10
Next, we observe how the terms change as we progress:
- From 1 to 4 is an increase of 3
- From 4 to 7 is an increase of 3
- From 7 to 10 is an increase of 3
This consistent increase indicates that this sequence is an arithmetic sequence where the common difference is 3. The first term (a) is 1, and the common difference (d) is 3.
The formula for the nth term of an arithmetic sequence can be defined as:
Tn = a + (n – 1) * d
Substituting the values of a and d into the formula:
Tn = 1 + (n – 1) * 3
Now, simplify the equation:
Tn = 1 + 3n – 3
Tn = 3n – 2
Thus, the nth term of the sequence can be expressed as Tn = 3n – 2. This formula allows you to find any term in the series by simply substituting the value of n.