What is the 12th term of the AP 96, 87, 78, ...?
Answer and explanation
Correct answer: −3
The governing formula for the nth term of an arithmetic progression is a_n=a_1+(n−1)d. Here the first term is a_1=96 and the common difference is d=87−96=−9. The negative difference confirms that each term decreases by 9. For the 12th term, eleven changes occur after the first term, so a_12=96+(12−1)(−9)=96−99=−3. Thus option A is correct. A common error is to use twelve differences, although the first term is already counted; that would produce the wrong value. Options B, C, and D also ignore the continued decrease or mishandle the negative sign. Substitution into the formula is the direct and reliable method.
Frequently asked questions
What is the correct answer to this question?
−3
Why is this the correct answer?
The governing formula for the nth term of an arithmetic progression is a_n=a_1+(n−1)d. Here the first term is a_1=96 and the common difference is d=87−96=−9. The negative difference confirms that each term decreases by 9. For the 12th term, eleven changes occur after the first term, so a_12=96+(12−1)(−9)=96−99=−3. Thus option A is correct. A common error is to use twelve differences, although the first term is already counted; that would produce the wrong value. Options B, C, and D also ignore the continued decrease or mishandle the negative sign. Substitution into the formula is the direct and reliable method.
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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