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Find the 58th term of the arithmetic sequence -28, -13, 2, ...−28,−13,2,...

1 Answer

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Final answer:

The 58th term of the arithmetic sequence starting with -28, -13, 2, is found using the formula for the nth term of an arithmetic sequence. With a common difference of 15, the 58th term is calculated to be 827.

Step-by-step explanation:

The student is asking for the 58th term of the arithmetic sequence that starts with the terms -28, -13, 2. To find this, we will use the formula for the nth term of an arithmetic sequence, which is:



an = a1 + (n - 1)d



Where a1 is the first term, d is the common difference, and n is the term number.



First, let's find the common difference. We subtract the first term from the second term:



d = -13 - (-28) = 15



Using the formula, the 58th term (a58) is calculated as follows:



a58 = -28 + (58 - 1) × 15



a58 = -28 + 57 × 15



a58 = -28 + 855



a58 = 827



Therefore, the 58th term of the sequence is 827.

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