To find the 31st term of the given sequence (9, 15, 21), we first need to analyze the pattern of the sequence.
1. **Identify the Pattern:** Let’s look at the differences between the consecutive terms:
- The difference between the 1st term (9) and the 2nd term (15) is 15 – 9 = 6.
- The difference between the 2nd term (15) and the 3rd term (21) is 21 – 15 = 6.
From this, we can see that this sequence increases by 6 each time. Thus, it is an arithmetic sequence.
2. **General Formula:** For an arithmetic sequence, the nth term can be calculated using the formula:
an = a1 + (n – 1) * d
Where:
- an is the nth term,
- a1 is the first term (9 in this case),
- d is the common difference (6),
- n is the term number.
3. **Calculate the 31st Term:** Now, we can substitute the values into the formula:
a31 = 9 + (31 – 1) * 6
a31 = 9 + 30 * 6
a31 = 9 + 180
a31 = 189
So, the 31st term of the sequence is 189.