what formula use in solving or finding for the 9th term of a number in arithmetic series and sequences?
term(9) = a + 8d
To find the nth term (also known as the general term) in an arithmetic sequence, you can use the formula:
𝑎𝑛 = 𝑎₁ + (𝑛 - 1)𝑑
Where:
- 𝑎𝑛 represents the nth term of the sequence.
- 𝑎₁ is the first term of the sequence.
- 𝑑 is the common difference between consecutive terms.
- 𝑛 is the position or number of the term you want to find.
To find the 9th term of a number in an arithmetic sequence, you'll need to know the first term (𝑎₁) and the common difference (𝑑). Plug these values into the formula and solve for 𝑎₉:
𝑎₉ = 𝑎₁ + (9 - 1)𝑑
Simplify the equation further:
𝑎₉ = 𝑎₁ + 8𝑑
Following these steps, you'll be able to find the 9th term of any arithmetic sequence.