In a game (20) points are earned at the first level and each next level gives (6) more points. How many points will be earned at the (18)th level?
Answer and explanation
Correct answer: 122
The scores form an arithmetic progression with first term \(a=20\), common difference \(d=6\), and \(n=18\). The nth term is \(a_n=a+(n-1)d\). Therefore, \(a_{18}=20+(18-1)\times6=20+102=122\). Hence, 122 points are earned at the 18th level. Getting 120 usually results from using the wrong number of intervals. Exam tip: for the nth term, add \(n-1\) common differences, not \(n\).
Frequently asked questions
What is the correct answer to this question?
122
Why is this the correct answer?
The scores form an arithmetic progression with first term \(a=20\), common difference \(d=6\), and \(n=18\). The nth term is \(a_n=a+(n-1)d\). Therefore, \(a_{18}=20+(18-1)\times6=20+102=122\). Hence, 122 points are earned at the 18th level. Getting 120 usually results from using the wrong number of intervals. Exam tip: for the nth term, add \(n-1\) common 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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