In the AP (7,12,17,\ldots), what is the last term less than (180)?
Answer and explanation
Correct answer: 177
Here, the first term is 7 and the common difference is 5. The nth term is \(a_n=7+5(n-1)\). From \(7+5(n-1)<180\), we get \(n<35.6\), so the greatest integer value of n is 35. Thus, \(a_{35}=7+5(34)=177\). The next term is 182, which is not less than 180. Although 179 is less than 180, it is not a term of this AP. 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?
177
Why is this the correct answer?
Here, the first term is 7 and the common difference is 5. The nth term is \(a_n=7+5(n-1)\). From \(7+5(n-1)<180\), we get \(n<35.6\), so the greatest integer value of n is 35. Thus, \(a_{35}=7+5(34)=177\). The next term is 182, which is not less than 180. Although 179 is less than 180, it is not a term of this AP. 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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