In the AP (18,25,32,\ldots), how many terms are less than (200)?
Answer and explanation
Correct answer: 26
Here, the first term is 18 and the common difference is 7. The nth term is 18+7(n-1). From 18+7(n-1)<200, we get 7n<189, so n<27. Hence, the greatest integer value of n is 26, and there are 26 terms less than 200. The 27th term is 200, so it is not included. Exam tip: For “less than”, do not count a term equal to the given limit.
Frequently asked questions
What is the correct answer to this question?
26
Why is this the correct answer?
Here, the first term is 18 and the common difference is 7. The nth term is 18+7(n-1). From 18+7(n-1)<200, we get 7n<189, so n<27. Hence, the greatest integer value of n is 26, and there are 26 terms less than 200. The 27th term is 200, so it is not included. Exam tip: For “less than”, do not count a term equal to the given limit.
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.
