To find the term number (n) in an arithmetic sequence, you can use the formula for the nth term and solve for n. According to the provided reference (0:22-4:05), the formula to achieve this is as follows:
an = a1 + (n - 1)d
Where:
- an is the nth term (the term you're trying to find the position of)
- a1 is the first term of the sequence
- n is the term number (what you want to find)
- d is the common difference between consecutive terms
To find 'n', you would rearrange the formula to solve for it:
- Start with the formula: an = a1 + (n - 1)d
- Subtract a1 from both sides: an - a1 = (n - 1)d
- Divide both sides by d: (an - a1) / d = n - 1
- Add 1 to both sides: (an - a1) / d + 1 = n
Therefore, the formula to find the term number (n) is:
n = (an - a1) / d + 1
This formula allows you to determine the position of any term within an arithmetic sequence, given the term itself, the first term, and the common difference.
