Find the indicated term of the arithmetic sequence with first term, and common difference, d. Find a₆₀ when a₁ = 35, d = -3.

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Identify the given information: the first term \(a_1 = 35\), the common difference \(d = -3\), and the term to find is the 60th term, \(a_{60}\).

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

Substitute the known values into the formula: \(a_{60} = 35 + (60 - 1) \times (-3)\).

Simplify the expression inside the parentheses: calculate \(60 - 1\) to get 59.

Multiply the common difference by 59 and then add the result to 35 to find \(a_{60}\).

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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.

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. In this problem, d = -3 means each term decreases by 3 from the previous term.

Formula for the nth Term of an Arithmetic Sequence

The nth term (a_n) of an arithmetic sequence is given by 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 calculation of any term, such as a_60, directly without listing all terms.

Find the indicated term of the arithmetic sequence with first term, and common difference, d. Find a60 when a1 = 35, d = -3.