Find the indicated term of the arithmetic sequence with first term, , and common difference, d. Find a₁₂ when a₁ = -8, d = -2

Verified step by step guidance

1. Identify the given values: the first term \(a_1 = -8\) and the common difference \(d = -2\).
2. Recall the formula for the \(n\)-th term of an arithmetic sequence: \(a_n = a_1 + (n - 1) \times d\).
3. Substitute \(n = 12\) into the formula to find the 12th term: \(a_{12} = a_1 + (12 - 1) \times d\).
4. Replace \(a_1\) and \(d\) with the given values: \(a_{12} = -8 + 11 \times (-2)\).
5. Simplify the expression step-by-step to find the value of \(a_{12}\).

Key Concepts

Arithmetic Sequence

An arithmetic sequence is a list of numbers where each term after the first is found by adding a constant difference to the previous term. This constant is called the common difference, and the sequence progresses linearly.

Common Difference (d)

The common difference is the fixed amount added to each term to get the next term in an arithmetic sequence. It can be positive, negative, or zero, and it determines the rate at which the sequence increases or decreases.

Formula for the nth Term of an Arithmetic Sequence

The nth term (a_n) of an arithmetic sequence can be found using the formula a_n = a_1 + (n - 1)d, where a_1 is the first term, d is the common difference, and n is the term number. This formula allows direct calculation of any term without listing all previous terms.