In an AP, a = 30 and d = −2. Which term will be 0?
Answer and explanation
Correct answer: 16th
For an arithmetic progression, the nth term is aₙ = a + (n − 1)d. We need aₙ = 0, with a = 30 and d = −2. Substitution gives 0 = 30 + (n − 1)(−2). Rearranging, 2(n − 1) = 30, so n − 1 = 15 and n = 16. Therefore the zero term is the 16th term, so option C is correct. The negative common difference means the terms decrease by 2: the 14th term is 4, the 15th is 2, and the 16th is 0. Option B stops one step early, while option D goes one step too far and gives −2. This direct check confirms both the index and the sign.
Frequently asked questions
What is the correct answer to this question?
16th
Why is this the correct answer?
For an arithmetic progression, the nth term is aₙ = a + (n − 1)d. We need aₙ = 0, with a = 30 and d = −2. Substitution gives 0 = 30 + (n − 1)(−2). Rearranging, 2(n − 1) = 30, so n − 1 = 15 and n = 16. Therefore the zero term is the 16th term, so option C is correct. The negative common difference means the terms decrease by 2: the 14th term is 4, the 15th is 2, and the 16th is 0. Option B stops one step early, while option D goes one step too far and gives −2. This direct check confirms both the index and the sign.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the $n$th term of an AP.
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