In a training plan (40) push-ups are done on the first day and (3) more push-ups are done each day. How many push-ups will be done on the (30)th day?
Answer and explanation
Correct answer: 127
This forms an arithmetic progression with first term \(a=40\), common difference \(d=3\), and \(n=30\). Using \(a_n=a+(n-1)d\), we get \(a_{30}=40+(30-1)\times3=40+87=127\). Therefore, 127 push-ups will be done on the 30th day. The option 130 results from incorrectly using \(n\) instead of \(n-1\). Exam tip: From the first term to the \(n\)th term, the common difference is added \(n-1\) times.
Frequently asked questions
What is the correct answer to this question?
127
Why is this the correct answer?
This forms an arithmetic progression with first term \(a=40\), common difference \(d=3\), and \(n=30\). Using \(a_n=a+(n-1)d\), we get \(a_{30}=40+(30-1)\times3=40+87=127\). Therefore, 127 push-ups will be done on the 30th day. The option 130 results from incorrectly using \(n\) instead of \(n-1\). Exam tip: From the first term to the \(n\)th term, the common difference is added \(n-1\) times.
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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