In Exercises 16–18, 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 formula for the nth term of an arithmetic sequence: \( a_n = a_1 + (n-1) \cdot d \).
2. Substitute the given values into the formula: \( a_{12} = -8 + (12-1) \cdot (-2) \).
3. Simplify the expression inside the parentheses: \( 12 - 1 = 11 \).
4. Multiply the common difference by the result from the previous step: \( 11 \cdot (-2) \).
5. Add the product to the first term: \( -8 + \text{(result from previous step)} \).

Key Concepts

Arithmetic Sequence

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is known as the common difference (d). The general form of an arithmetic sequence can be expressed as a_n = a_1 + (n - 1)d, where a_n is the nth term, a_1 is the first term, and n is the term number.

First Term and Common Difference

In an arithmetic sequence, the first term (a_1) is the initial value from which the sequence starts. The common difference (d) is the fixed amount added to each term to obtain the next term. For example, if a_1 = -8 and d = -2, each subsequent term is found by subtracting 2 from the previous term.

Finding a Specific Term

To find a specific term in an arithmetic sequence, you can use the formula a_n = a_1 + (n - 1)d. By substituting the values of a_1, d, and n into this formula, you can calculate the desired term. For instance, to find a_12, you would substitute n = 12, a_1 = -8, and d = -2 into the formula.