A craftsperson makes (8) toys on the first day and (2) more toys each next day. How many toys are made on the (12)th day?
Answer and explanation
Correct answer: 30
This is an arithmetic progression with first term \(a=8\), common difference \(d=2\), and \(n=12\). The \(n\)th term is \(a_n=a+(n-1)d\). Therefore, \(a_{12}=8+(12-1)\times2=8+22=30\). Hence, 30 toys are made on the 12th day. Adding \(12\times2\) to 8 would incorrectly give 32, because the increase occurs only 11 times after the first day. Exam tip: use \((n-1)d\), not \(nd\), for the \(n\)th term of an AP.
Frequently asked questions
What is the correct answer to this question?
30
Why is this the correct answer?
This is an arithmetic progression with first term \(a=8\), common difference \(d=2\), and \(n=12\). The \(n\)th term is \(a_n=a+(n-1)d\). Therefore, \(a_{12}=8+(12-1)\times2=8+22=30\). Hence, 30 toys are made on the 12th day. Adding \(12\times2\) to 8 would incorrectly give 32, because the increase occurs only 11 times after the first day. Exam tip: use \((n-1)d\), not \(nd\), for the \(n\)th term of an AP.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Word problems based on APs.
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