What is the sum of the first 7 terms of the arithmetic progression (18, 24, 30, ...)?
Answer and explanation
Correct answer: 252
The first term is a = 18 and the common difference is d = 24 - 18 = 6. The seventh term is a_7 = a + (7 - 1)d = 18 + 6 × 6 = 54. Using the average-of-end-terms method, S_7 = 7/2(18 + 54) = 7/2 × 72 = 7 × 36 = 252. Therefore option B is correct. The sum formula gives the same result: 7/2[2(18) + 6(6)] = 7/2(72) = 252. The nearby values are distractors from incorrect multiplication or an incorrect final term.
Frequently asked questions
What is the correct answer to this question?
252
Why is this the correct answer?
The first term is a = 18 and the common difference is d = 24 - 18 = 6. The seventh term is a_7 = a + (7 - 1)d = 18 + 6 × 6 = 54. Using the average-of-end-terms method, S_7 = 7/2(18 + 54) = 7/2 × 72 = 7 × 36 = 252. Therefore option B is correct. The sum formula gives the same result: 7/2[2(18) + 6(6)] = 7/2(72) = 252. The nearby values are distractors from incorrect multiplication or an incorrect final term.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the sum of the first $n$ terms of an AP.
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