The first term of an AP is 4, and its 8th term is 3 times its 3rd term. What is the sum of the first 12 terms?
Answer and explanation
Correct answer: 576
The governing concept is the general term of an AP, aₙ = a + (n - 1)d, followed by the AP sum formula. Since a = 4, the 8th term is 4 + 7d and the 3rd term is 4 + 2d. The condition gives 4 + 7d = 3(4 + 2d), so 4 + 7d = 12 + 6d and d = 8. Now use S₁₂ = 12/2 [2(4) + 11(8)] = 6(8 + 88) = 6 × 96 = 576. Therefore option C is correct. The other options arise from using an incorrect position difference, treating the third term as 3d, or substituting the wrong common difference into the sum formula.
Frequently asked questions
What is the correct answer to this question?
576
Why is this the correct answer?
The governing concept is the general term of an AP, aₙ = a + (n - 1)d, followed by the AP sum formula. Since a = 4, the 8th term is 4 + 7d and the 3rd term is 4 + 2d. The condition gives 4 + 7d = 3(4 + 2d), so 4 + 7d = 12 + 6d and d = 8. Now use S₁₂ = 12/2 [2(4) + 11(8)] = 6(8 + 88) = 6 × 96 = 576. Therefore option C is correct. The other options arise from using an incorrect position difference, treating the third term as 3d, or substituting the wrong common difference into the sum formula.
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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