This question is a bit unclear. It seems to imply a sequence generated by multiplying, but the provided reference refers to an arithmetic sequence, which is generated by adding a constant difference. Therefore, I will address both interpretations: arithmetic sequences and geometric sequences (where you multiply).
1. Finding the nth Term of an Arithmetic Sequence (Constant Difference)
If you are referring to an arithmetic sequence, where each term is found by adding a constant value (the common difference), then the formula to find the nth term is:
*an = a1 + (n - 1) d**
Where:
- an is the nth term you want to find.
- a1 is the first term of the sequence.
- n is the term number you are looking for (e.g., 5th term, 10th term, etc.).
- d is the common difference between consecutive terms.
Example:
Consider the arithmetic sequence: 2, 5, 8, 11, ...
- a1 = 2 (the first term)
- d = 3 (the common difference: 5-2 = 3, 8-5 = 3, etc.)
To find the 7th term (a7):
a7 = 2 + (7 - 1) 3
a7 = 2 + (6) 3
a7 = 2 + 18
a7 = 20
Therefore, the 7th term of the sequence is 20.
2. Finding the nth Term of a Geometric Sequence (Constant Ratio)
If you are referring to a geometric sequence, where each term is found by multiplying by a constant value (the common ratio), then the formula to find the nth term is:
*an = a1 r(n - 1)**
Where:
- an is the nth term you want to find.
- a1 is the first term of the sequence.
- n is the term number you are looking for.
- r is the common ratio between consecutive terms.
Example:
Consider the geometric sequence: 3, 6, 12, 24, ...
- a1 = 3 (the first term)
- r = 2 (the common ratio: 6/3 = 2, 12/6 = 2, etc.)
To find the 5th term (a5):
a5 = 3 2(5 - 1)
a5 = 3 24
a5 = 3 * 16
a5 = 48
Therefore, the 5th term of the sequence is 48.
In summary, to find the nth term, you need to identify if the sequence is arithmetic (addition/subtraction) or geometric (multiplication/division) and then apply the appropriate formula.
