Write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for a_n to find a₂₀, the 20th term of the sequence. a₁=-20, d = -4

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Recall that the general term (nth term) of an arithmetic sequence can be written as \(a_n = a_1 + (n - 1)d\), where \(a_1\) is the first term and \(d\) is the common difference.

Identify the given values: the first term \(a_1 = -20\) and the common difference \(d = -4\).

Substitute these values into the general term formula to get \(a_n = -20 + (n - 1)(-4)\).

Simplify the expression inside the parentheses: \(a_n = -20 - 4(n - 1)\).

To find the 20th term, substitute \(n = 20\) into the formula: \(a_{20} = -20 - 4(20 - 1)\).

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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 (d). Understanding this pattern is essential to write formulas and find specific terms.

General Term Formula of an Arithmetic Sequence

The general term (nth term) of an arithmetic sequence is given by the formula an = a1 + (n - 1)d, where a1 is the first term, d is the common difference, and n is the term number. This formula allows direct calculation of any term without recursion.

Evaluating the nth Term

Once the general term formula is established, substituting the desired term number (like n=20) into the formula yields the specific term's value. This step involves simple arithmetic and is crucial for solving problems that ask for a particular term.

Write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for an to find a20, the 20th term of the sequence. a1=-20, d = -4