Find the (18)th term of the AP (35,30,25,20,\ldots).
Answer and explanation
Correct answer: \(-50\)
For this AP, the first term is \(a=35\) and the common difference is \(d=30-35=-5\). The \(n\)th term is given by \(a_n=a+(n-1)d\). Thus, \(a_{18}=35+(18-1)(-5)=35-85=-50\). Hence, \(-50\) is correct. A value such as \(-48\) results from not applying the common difference \(-5\) the required number of times. Exam tip: use \(n-1\) gaps, not \(n\), when finding the \(n\)th term.
Frequently asked questions
What is the correct answer to this question?
\(-50\)
Why is this the correct answer?
For this AP, the first term is \(a=35\) and the common difference is \(d=30-35=-5\). The \(n\)th term is given by \(a_n=a+(n-1)d\). Thus, \(a_{18}=35+(18-1)(-5)=35-85=-50\). Hence, \(-50\) is correct. A value such as \(-48\) results from not applying the common difference \(-5\) the required number of times. Exam tip: use \(n-1\) gaps, not \(n\), when finding the \(n\)th term.
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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