What is the general formula of finding the nth term of an arithmetic sequence?

The general formula for finding the nth term of an arithmetic sequence is: a_n = a₁ + (n - 1)d

Here's a breakdown of what each component represents:

• a_n: The nth term of the sequence (the term you want to find).
• a₁: The first term of the sequence.
• n: The position of the term you want to find in the sequence (e.g., 3rd term, 10th term).
• d: The common difference between consecutive terms in the sequence.

Explanation:

An arithmetic sequence is a sequence of numbers where the difference between any two consecutive terms is constant. This constant difference is called the common difference (d).

The formula essentially says that to find the nth term, you start with the first term (a₁) and add the common difference (d) a certain number of times. That "certain number of times" is (n-1), because to get to the second term, you only add the difference once, to get to the third term you add the difference twice, and so on.

Example:

Consider the arithmetic sequence: 2, 5, 8, 11, 14,...

• a₁ = 2 (the first term)
• d = 3 (the common difference; 5-2 = 3, 8-5 = 3, etc.)

Let's say you want to find the 7th term (a₇). Using the formula:

a₇ = a₁ + (n - 1)d
a₇ = 2 + (7 - 1)3
a₇ = 2 + (6)3
a₇ = 2 + 18
a₇ = 20

Therefore, the 7th term of the sequence is 20.