Find the indicated term of the arithmetic sequence with first term, and common difference, d. Find a₅₀ when a₁ = 7, d = 5.

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Identify the given information: the first term \(a_1 = 7\) 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 \(n = 50\) into the formula to find the 50th term: \(a_{50} = 7 + (50 - 1) \times 5\).

Simplify the expression inside the parentheses: calculate \(50 - 1\).

Multiply the result by the common difference \(5\) and then add the first term \(7\) to find \(a_{50}\).

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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. Knowing d allows you to calculate any term in the sequence using the formula for the nth term.

Formula for the nth Term of an Arithmetic Sequence

The nth term (a_n) of an arithmetic sequence is given by a_n = a₁ + (n - 1)d, where a₁ is the first term, d is the common difference, and n is the term number. This formula is essential for finding specific terms like a₅₀ without listing all previous terms.

Find the indicated term of the arithmetic sequence with first term, and common difference, d. Find a50 when a1 = 7, d = 5.