What is the sum of the first 8 terms of the arithmetic progression (10, 17, 24, 31, ...)?
Answer and explanation
Correct answer: 276
Use the arithmetic-progression sum formula S_n = n/2 [2a + (n - 1)d]. The first term is a = 10, the common difference is d = 17 - 10 = 7, and the required number of terms is n = 8. Therefore S_8 = 8/2 [2(10) + (8 - 1)(7)] = 4[20 + 49] = 4×69 = 276. Hence option B is correct. A useful check is to find the eighth term: a_8 = 10 + 7×7 = 59. The average of the first and last terms is (10 + 59)/2 = 34.5, and 8×34.5 = 276. The other choices do not satisfy this calculation.
Frequently asked questions
What is the correct answer to this question?
276
Why is this the correct answer?
Use the arithmetic-progression sum formula S_n = n/2 [2a + (n - 1)d]. The first term is a = 10, the common difference is d = 17 - 10 = 7, and the required number of terms is n = 8. Therefore S_8 = 8/2 [2(10) + (8 - 1)(7)] = 4[20 + 49] = 4×69 = 276. Hence option B is correct. A useful check is to find the eighth term: a_8 = 10 + 7×7 = 59. The average of the first and last terms is (10 + 59)/2 = 34.5, and 8×34.5 = 276. The other choices do not satisfy this calculation.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Arithmetic Progression.
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