In an AP, d = −11 and S₄₁ = 0. What is the first term a?
Answer and explanation
Correct answer: 220
The sum of the first n terms of an AP is Sₙ = n/2[2a + (n − 1)d]. For n = 41, d = −11, and S₄₁ = 0, substitute the values: 0 = 41/2[2a + 40(−11)] = 41/2(2a − 440). Since 41/2 is non-zero, the bracket must equal zero. Thus 2a − 440 = 0, so 2a = 440 and a = 220. Therefore option C is correct. The zero total does not mean that a is zero; it means the positive and negative terms cancel overall. The other choices come from mishandling the 40d term or dividing incorrectly.
Frequently asked questions
What is the correct answer to this question?
220
Why is this the correct answer?
The sum of the first n terms of an AP is Sₙ = n/2[2a + (n − 1)d]. For n = 41, d = −11, and S₄₁ = 0, substitute the values: 0 = 41/2[2a + 40(−11)] = 41/2(2a − 440). Since 41/2 is non-zero, the bracket must equal zero. Thus 2a − 440 = 0, so 2a = 440 and a = 220. Therefore option C is correct. The zero total does not mean that a is zero; it means the positive and negative terms cancel overall. The other choices come from mishandling the 40d term or dividing incorrectly.
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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