What is the (18)th term of the AP (64,60,56,52,\ldots)?
Answer and explanation
Correct answer: \(-4\)
For this AP, the first term is \(a=64\) and the common difference is \(d=60-64=-4\). The \(n\)th term is given by \(a_n=a+(n-1)d\). Therefore, \(a_{18}=64+(18-1)(-4)=64-68=-4\). Hence, \(-4\) is correct. The close distractor \(-2\) is incorrect because adding \(-4\) 17 times decreases 64 by \(68\). Exam tip: Always use \(n-1\), not \(n\), in the nth-term formula.
Frequently asked questions
What is the correct answer to this question?
\(-4\)
Why is this the correct answer?
For this AP, the first term is \(a=64\) and the common difference is \(d=60-64=-4\). The \(n\)th term is given by \(a_n=a+(n-1)d\). Therefore, \(a_{18}=64+(18-1)(-4)=64-68=-4\). Hence, \(-4\) is correct. The close distractor \(-2\) is incorrect because adding \(-4\) 17 times decreases 64 by \(68\). Exam tip: Always use \(n-1\), not \(n\), in the nth-term formula.
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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