What is the sum of the first 18 terms of the arithmetic progression −12, −5, 2, …?
Answer and explanation
Correct answer: 855
The correct answer is C, 855. The first term is a = −12, and the common difference is d = −5 − (−12) = 7. Use the sum formula S_n = n/2[2a + (n−1)d]. For n = 18, S_18 = 18/2[2(−12) + 17(7)] = 9[−24 + 119] = 9 × 95 = 855. The negative first term does not make the total negative because the sequence increases by 7 and later terms are positive; the last term is −12 + 17(7) = 107. Options 805, 830 and 880 arise from an incorrect difference, a wrong number of intervals, or an arithmetic error in the bracket.
Frequently asked questions
What is the correct answer to this question?
855
Why is this the correct answer?
The correct answer is C, 855. The first term is a = −12, and the common difference is d = −5 − (−12) = 7. Use the sum formula S_n = n/2[2a + (n−1)d]. For n = 18, S_18 = 18/2[2(−12) + 17(7)] = 9[−24 + 119] = 9 × 95 = 855. The negative first term does not make the total negative because the sequence increases by 7 and later terms are positive; the last term is −12 + 17(7) = 107. Options 805, 830 and 880 arise from an incorrect difference, a wrong number of intervals, or an arithmetic error in the bracket.
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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