In the AP (2,6,10,\ldots), what is the last term less than (75)?
Answer and explanation
Correct answer: 74
Here, the first term is 2 and the common difference is 4. Thus, \(a_n=2+4(n-1)=4n-2\). From \(4n-2<75\), we get \(n<19.25\), so the greatest integer value of n is 19. Therefore, \(a_{19}=74\), which is the last term less than 75. The next term, 76, is not less than 75. Exam tip: For a “last term less than” question, solve the inequality and take the greatest possible integer value of n.
Frequently asked questions
What is the correct answer to this question?
74
Why is this the correct answer?
Here, the first term is 2 and the common difference is 4. Thus, \(a_n=2+4(n-1)=4n-2\). From \(4n-2<75\), we get \(n<19.25\), so the greatest integer value of n is 19. Therefore, \(a_{19}=74\), which is the last term less than 75. The next term, 76, is not less than 75. Exam tip: For a “last term less than” question, solve the inequality and take 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.
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