Use the formula $a_n=4+(n-1)(-7)$ to find the eighth term of the sequence $4,-3,-10,\dots$

Verified step by step guidance

1. Identify the given formula for the nth term of the sequence: $a{n}_{}=4+(n-1)(-7)$.
2. Recognize that to find the eighth term, you need to substitute $n=8$ into the formula.
3. Substitute $8$ for $n$ in the formula: $a{8}_{}=\; 4\; +\; (8\; -\; 1)(-7)$.
4. Simplify the expression inside the parentheses: calculate $8\; -\; 1$ to get $7$.
5. Multiply $7$ by $-7$ and then add $4$ to find the value of the eighth term.

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. Understanding this helps identify the pattern and predict future terms.

General Term Formula of an Arithmetic Sequence

The formula a_n = a_1 + (n - 1)d gives the nth term of an arithmetic sequence, 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.

Substitution and Evaluation

To find a specific term using the formula, substitute the term number (n) into the formula and perform arithmetic operations carefully. This step requires accurate substitution and simplification to get the correct term value.