Find the (14)th term of the AP (33,29,25,21,\ldots).
Answer and explanation
Correct answer: \(-19\)
The first term is \(a=33\), and the common difference is \(d=29-33=-4\). The \(n\)th term is given by \(a_n=a+(n-1)d\). Therefore, \(a_{14}=33+(14-1)(-4)=33-52=-19\). Hence, \(-19\) is correct. The value \(-17\) results from adding \(-4\) only 12 times, which gives the 13th term. Exam tip: Always use \(n-1\), not \(n\), in the nth-term formula.
Frequently asked questions
What is the correct answer to this question?
\(-19\)
Why is this the correct answer?
The first term is \(a=33\), and the common difference is \(d=29-33=-4\). The \(n\)th term is given by \(a_n=a+(n-1)d\). Therefore, \(a_{14}=33+(14-1)(-4)=33-52=-19\). Hence, \(-19\) is correct. The value \(-17\) results from adding \(-4\) only 12 times, which gives the 13th term. 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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