Write the first six terms of each arithmetic sequence. a₁ = 200, d = 20

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Recall that an arithmetic sequence is a sequence of numbers where each term after the first is found by adding a constant difference \(d\) to the previous term.

The formula for the \(n\)-th term of an arithmetic sequence is given by: \[a_n = a_1 + (n - 1) \times d\]

Given the first term \(a_1 = 200\) and the common difference \(d = 20\), substitute these values into the formula to find each term.

Calculate the first six terms by plugging in \(n = 1, 2, 3, 4, 5, 6\) into the formula: \[a_1 = 200 + (1 - 1) \times 20\] \[a_2 = 200 + (2 - 1) \times 20\] \[a_3 = 200 + (3 - 1) \times 20\] \[a_4 = 200 + (4 - 1) \times 20\] \[a_5 = 200 + (5 - 1) \times 20\] \[a_6 = 200 + (6 - 1) \times 20\]

Write out the six terms you get from these calculations to complete the first six terms of the arithmetic sequence.

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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 difference is called the common difference, denoted by d. Understanding this helps in generating terms of 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 = 20 means each term increases by 20 from the previous one.

Formula for the nth Term

The nth term of an arithmetic sequence can be found using the formula aₙ = a₁ + (n - 1)d, where a₁ is the first term and d is the common difference. This formula allows calculation of any term without listing all previous terms.

Write the first six terms of each arithmetic sequence. a1 = 200, d = 20