What is the greatest term less than (100) in the AP (1,4,7,\ldots)?
Answer and explanation
Correct answer: 97
Here, the first term is 1 and the common difference is 3, so the nth term is \(a_n=1+3(n-1)=3n-2\). From \(3n-2<100\), we get \(n<34\); hence the greatest integral value of n is \(33\). Therefore, \(a_{33}=97\). Although 99 is less than 100, it is not a term of this AP because the terms increase by 3 from 1. Exam tip: write \(a_n<\) the given number and find the greatest possible integer value of n.
Frequently asked questions
What is the correct answer to this question?
97
Why is this the correct answer?
Here, the first term is 1 and the common difference is 3, so the nth term is \(a_n=1+3(n-1)=3n-2\). From \(3n-2<100\), we get \(n<34\); hence the greatest integral value of n is \(33\). Therefore, \(a_{33}=97\). Although 99 is less than 100, it is not a term of this AP because the terms increase by 3 from 1. Exam tip: write \(a_n<\) the given number and find the greatest possible integer value of n.
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.
