If the arithmetic sequence has a first term a_1 = 7 and a common difference d = 4, what is the sum of the first 25 terms (S_25)?
Answer and explanation
Correct answer: D. 1,375
- Step 1: The sum of the first n terms of an arithmetic sequence is given by: S_n = (n / 2) * [2a_1 + (n - 1)d].
- Step 2: Here, n = 25, a_1 = 7, and d = 4.
- Step 3: Compute inside the brackets: 2(7) + (25 - 1)(4) = 14 + (24)(4) = 14 + 96 = 110.
- Step 4: Calculate the sum: S_25 = (25 / 2) 110 = 25 55 = 1,375.
Answer
1,375.
Why not the others: '1,250' uses a_1 = 0; '1,450' uses d = 5; '2,750' forgets to divide by 2.
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