How many terms are there up to (72) in the arithmetic progression (7,12,17,\ldots)?
Answer and explanation
Correct answer: 14
Here, the first term is \(a=7\) and the common difference is \(d=5\). The \(n\)th term is \(a_n=a+(n-1)d\). So, \(72=7+(n-1)\times5\), giving \(65=5(n-1)\), hence \(n-1=13\) and \(n=14\). Therefore, 72 is the 14th term of the AP. The 13th term is 67, so 13 is not correct. Exam tip: When the last term is given, equate it to \(a_n\) and solve for \(n\).
Frequently asked questions
What is the correct answer to this question?
14
Why is this the correct answer?
Here, the first term is \(a=7\) and the common difference is \(d=5\). The \(n\)th term is \(a_n=a+(n-1)d\). So, \(72=7+(n-1)\times5\), giving \(65=5(n-1)\), hence \(n-1=13\) and \(n=14\). Therefore, 72 is the 14th term of the AP. The 13th term is 67, so 13 is not correct. Exam tip: When the last term is given, equate it to \(a_n\) and solve for \(n\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Arithmetic Progression.
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