An arithmetic sequence has first term [math: 400] and third term [math: 610] . The [math: 10th] 10^{th} term of this sequence is:

Question

An arithmetic sequence has first term [math: 400] and third term [math: 610] .  The [math: 10th] 10^{th} term of this sequence is:

BlackTom AI · Accepted Answer

We’re given an arithmetic sequence with first term a1 = 400 and third term a3 = 610. In an arithmetic sequence, each term increases by a common difference d, so a3 = a1 + 2d.

Option A: 1450. If we test this against the pattern, we’d need a10 to be 1450. From the information given, the difference d is determined by 610 = 400 + 2d, so d = (610 − 400)/2 = 105. Then a10 = a1 + 9d = 400 + 9×105 = 400 + 945 = 1345. Since 1450 ≠ 1345, this option does not match the sequence’s actual 10th term.

Option B: 1030. Using the same computed d = 105, we get a10 = 400 + 9×105 = 1345, not 1030. Therefore this value is inconsistent with the sequence defined by a1 = 400 and a3 = 610.

Option C: 1540. With d = 105, the 10th term is 1345, not 1540. This option similarly conflicts with the established pattern of increments.

Option D: 1345. Computing from the given first and third terms, d = (610 − 400)/2 = 105, and a10 = a1 + 9d = 400 + 9×105 = 400 + 945 = 1345. This value aligns with the derived common difference and the starting term, fitting the arithmetic sequence.

Summary thought process: determine the common difference from a3 = a1 + 2d, then project to a10 using a10 = a1 + 9d. Options A, B, and C yield values that do not match the calculated a10, while option D matches exactly.

MUF0141 Fund. Mathematics Unit 1 - Semester 2, 2025

An arithmetic sequence has first term [math: 400] and third term [math: 610] . The [math: 10th] 10^{th} term of this sequence is:

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