Find the (10)th term of the AP (45,39,33,27,\ldots).
Answer and explanation
Correct answer: -9
For this AP, the first term is \(a=45\) and the common difference is \(d=39-45=-6\). The \(n\)th term is given by \(a_n=a+(n-1)d\). Thus, \(a_{10}=45+(10-1)(-6)=45-54=-9\). Therefore, \(-9\) is correct. Choosing \(-3\) results from using the number of differences incorrectly. Exam tip: for the \(n\)th term, use \(n-1\) differences, not \(n\).
Frequently asked questions
What is the correct answer to this question?
-9
Why is this the correct answer?
For this AP, the first term is \(a=45\) and the common difference is \(d=39-45=-6\). The \(n\)th term is given by \(a_n=a+(n-1)d\). Thus, \(a_{10}=45+(10-1)(-6)=45-54=-9\). Therefore, \(-9\) is correct. Choosing \(-3\) results from using the number of differences incorrectly. Exam tip: for the \(n\)th term, use \(n-1\) differences, not \(n\).
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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