Which term of the AP (14,23,32,\ldots) is (185)?
Answer and explanation
Correct answer: (20)th
For an arithmetic progression, the nth term is given by a_n=a+(n-1)d, where a is the first term and d is the common difference. Here a=14 and d=23-14=9. To find which term equals 185, substitute these values: 185=14+(n-1)9. Subtracting 14 gives 171=9(n-1), and dividing by 9 gives n-1=19. Therefore n=20.
A direct check is also useful. The twentieth term is 14+19×9=14+171=185, so the number is reached exactly at the twentieth position. Thus option C, the 20th term, is correct. The 19th term would be 176 and the 21st term would be 194, so neither neighboring option can represent 185. The common difference must be used with n-1, because the first term already corresponds to n=1.
Frequently asked questions
What is the correct answer to this question?
(20)th
Why is this the correct answer?
For an arithmetic progression, the nth term is given by a_n=a+(n-1)d, where a is the first term and d is the common difference. Here a=14 and d=23-14=9. To find which term equals 185, substitute these values: 185=14+(n-1)9. Subtracting 14 gives 171=9(n-1), and dividing by 9 gives n-1=19. Therefore n=20.
A direct check is also useful. The twentieth term is 14+19×9=14+171=185, so the number is reached exactly at the twentieth position. Thus option C, the 20th term, is correct. The 19th term would be 176 and the 21st term would be 194, so neither neighboring option can represent 185. The common difference must be used with n-1, because the first term already corresponds to n=1.
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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