What is the (16)th term of the AP (200,190,180,170,\ldots)?
Answer and explanation
Correct answer: 50
In this AP, the first term is \(a=200\) and the common difference is \(d=190-200=-10\). Using \(a_n=a+(n-1)d\), we get \(a_{16}=200+(16-1)(-10)=200-150=50\). Hence, 50 is correct. Choosing 60 would count only 14 differences, whereas there are 15 differences from the first term to the 16th term. Exam tip: always use \(n-1\) in the nth-term formula and keep track of a negative common difference.
Frequently asked questions
What is the correct answer to this question?
50
Why is this the correct answer?
In this AP, the first term is \(a=200\) and the common difference is \(d=190-200=-10\). Using \(a_n=a+(n-1)d\), we get \(a_{16}=200+(16-1)(-10)=200-150=50\). Hence, 50 is correct. Choosing 60 would count only 14 differences, whereas there are 15 differences from the first term to the 16th term. Exam tip: always use \(n-1\) in the nth-term formula and keep track of a negative common difference.
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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