The sum of the first ten terms of the arithmetic sequence 5, 7, 9, … is:

Question

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We are given an arithmetic sequence with first term a1 = 5 and common difference d = 2.

First, recall the formula for the sum of the first n terms of an arithmetic sequence: S_n = n/2 [2a1 + (n − 1)d]. Here n = 10, so:

S_10 = 10/2 [2(5) + (10 − 1)(2)] = 5 [10 + 9×2] = 5 [10 + 18] = 5 × 28 = 140.

Now evaluate the answer choices:

- Option a: 85. This would require a sum significantly smaller than 140; checking the calculation shows 85 would correspond to a much smaller cumulative total, so this is not correct given the actual sum is 140.
- Option b: 100. Similarly, 100 is not equal to the computed 140, and there is no small alteration that would bring the 10-term sum exactly to 100 with the stated a1 and d.
- Option c: 140. This matches the computed sum S_10 = 140, so this is consistent with the formula and the given sequence.
- Option d: 115. Like 85 and 100, 115 does not align with the precise arithmetic progression sum for the first ten terms and would require a different set of parameters or a different n.

In summary, the only value that aligns with the sum formula for the provided first term and common difference over ten terms is 140; the other options conflict with the exact calculation.

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

The sum of the first ten terms of the arithmetic sequence 5, 7, 9, … is:

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