Find the indicated term of the arithmetic sequence with first term, and common difference, d. Find a₂₀₀ when a₁ = −40, d = 5.

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Identify the given information: the first term \(a_1 = -40\) and the common difference \(d = 5\).

Recall the formula for the \(n\)-th term of an arithmetic sequence: \(a_n = a_1 + (n - 1) \times d\).

Substitute the values into the formula for \(n = 200\): \(a_{200} = -40 + (200 - 1) \times 5\).

Simplify the expression inside the parentheses: calculate \(200 - 1\).

Multiply the result by the common difference \(5\) and then add \(-40\) to find \(a_{200}\).

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주요 개념

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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, denoted by d. Understanding this helps identify the pattern and predict any term in the sequence.

General Formula for the nth Term

The nth term 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.

Substitution and Evaluation

To find a specific term like a_200, substitute the given values of a_1, d, and n into the nth term formula. Then perform arithmetic operations carefully to evaluate the term accurately. This step is essential for solving the problem correctly.

Find the indicated term of the arithmetic sequence with first term, and common difference, d. Find a200 when a1 = −40, d = 5.