To find the 25th term of the arithmetic sequence 3, 9, 15, 21, 27, we first need to identify the pattern of the sequence.
An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant. In this case, we can calculate the common difference:
- 9 – 3 = 6
- 15 – 9 = 6
- 21 – 15 = 6
- 27 – 21 = 6
So, the common difference (d) is 6.
The formula for the n-th term (Tn) of an arithmetic sequence can be expressed as:
Tn = a + (n - 1) * d
Where:
- Tn is the n-th term of the sequence.
- a is the first term of the sequence.
- n is the term number.
- d is the common difference.
In our sequence:
- a = 3 (the first term)
- d = 6 (the common difference)
- n = 25 (the term we want)
Now we can substitute these values into the formula:
T25 = 3 + (25 - 1) * 6
This simplifies to:
T25 = 3 + 24 * 6
T25 = 3 + 144
T25 = 147
Therefore, the 25th term of the arithmetic sequence is 147.