The 10th term in the sequence 2, 5, 8, … is:

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The sequence given is 2, 5, 8, … which increases by a constant amount each step.

First, identify the pattern: each term adds 3 to the previous term, so it is an arithmetic sequence with first term a1 = 2 and common difference d = 3.

Now consider each option:

- Option a: 26. If a_n = 26, then 26 = 2 + (n − 1)·3. This gives (n − 1)·3 = 24, so n − 1 = 8 and n = 9. That would place 26 at the 9th position, not the 10th. Therefore this is not the 10th term.

- Option b: 40. Setting 40 = 2 + (n − 1)·3 yields (n − 1)·3 = 38, so n − 1 = 38/3, which is not an integer. Since n must be an integer position, 40 cannot be any term in this sequence.

- Option c: 32. Solve 32 = 2 + (n − 1)·3. Then (n − 1)·3 = 30, so n − 1 = 10 and n = 11. That would place 32 at the 11th term, not the 10th.

- Option d: 29. Solve 29 = 2 + (n − 1)·3. Then (n − 1)·3 = 27, so n − 1 = 9 and n = 10. This correctly identifies 29 as the 10th term of the sequence.

In summary, only option d yields an integer position matching the 10th term for an arithmetic sequence with a1 = 2 and d = 3, while the other options correspond to different term positions or are not terms at all.

MUF0141 Fund. Mathematics Unit 1 - Semester 2, 2025 5.6 Arithmetic Sequences Quiz (Formative)

The 10th term in the sequence 2, 5, 8, … is:

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