Which expression correctly gives the nth term of an arithmetic sequence with first term a1 and common difference d?

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Multiple Choice

Which expression correctly gives the nth term of an arithmetic sequence with first term a1 and common difference d?

Explanation:
In an arithmetic sequence, each step adds the same amount d to the previous term. To reach the nth term from the first term a1, you’ve taken n-1 steps, so you add (n-1)d to a1. That gives the nth term as a1 + (n-1)d. For example, with a1 = 5 and d = 3, the sequence goes 5, 8, 11, 14, and the fourth term is 5 + 3(4−1) = 14. The other expressions fail basic checks: a1 + nd would not yield a1 when n = 1; a1 + (n-2)d misplaces the starting term; and a1 + d is a fixed amount, not depending on n.

In an arithmetic sequence, each step adds the same amount d to the previous term. To reach the nth term from the first term a1, you’ve taken n-1 steps, so you add (n-1)d to a1. That gives the nth term as a1 + (n-1)d. For example, with a1 = 5 and d = 3, the sequence goes 5, 8, 11, 14, and the fourth term is 5 + 3(4−1) = 14. The other expressions fail basic checks: a1 + nd would not yield a1 when n = 1; a1 + (n-2)d misplaces the starting term; and a1 + d is a fixed amount, not depending on n.

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