What is the (12)th term of the AP (100,90,80,70,\ldots)?
Answer and explanation
Correct answer: -10
In this AP, the first term is \(a=100\) and the common difference is \(d=90-100=-10\). The \(n\)th term is \(a_n=a+(n-1)d\). Therefore, \(a_{12}=100+(12-1)(-10)=100-110=-10\). Option 0 is the 11th term, as it uses only 10 common differences from the first term. Exam tip: for the \(n\)th term, use \(n-1\), not \(n\), differences.
Frequently asked questions
What is the correct answer to this question?
-10
Why is this the correct answer?
In this AP, the first term is \(a=100\) and the common difference is \(d=90-100=-10\). The \(n\)th term is \(a_n=a+(n-1)d\). Therefore, \(a_{12}=100+(12-1)(-10)=100-110=-10\). Option 0 is the 11th term, as it uses only 10 common differences from the first term. Exam tip: for the \(n\)th term, use \(n-1\), not \(n\), differences.
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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