If \(a_n=5n+s\) and \(a_{18}=112\), what is \(a_{46}\)?
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Answer and explanation
Correct answer: \(252\)
Given \(a_n=5n+s\), we have \(a_{18}=5\times18+s=90+s\). Since \(a_{18}=112\), \(s=22\). Therefore, \(a_{46}=5\times46+22=230+22=252\). Option \(247\) would result from incorrectly taking 27 gaps; actually, \(46-18=28\). Exam tip: You may also use \(a_{46}=a_{18}+(46-18)d\), where \(d=5\).
Frequently asked questions
What is the correct answer to this question?
\(252\)
Why is this the correct answer?
Given \(a_n=5n+s\), we have \(a_{18}=5\times18+s=90+s\). Since \(a_{18}=112\), \(s=22\). Therefore, \(a_{46}=5\times46+22=230+22=252\). Option \(247\) would result from incorrectly taking 27 gaps; actually, \(46-18=28\). Exam tip: You may also use \(a_{46}=a_{18}+(46-18)d\), where \(d=5\).
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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