In a garden the first row has (21) plants and each next row has (11) more plants. Which row will have (252) plants?
Answer and explanation
Correct answer: 22
The numbers of plants form an arithmetic progression with first term \(a=21\) and common difference \(d=11\). The number of plants in the \(n\)th row is \(a_n=21+(n-1)\times 11\). Setting this equal to 252 gives \(21+(n-1)\times 11=252\), so \(11(n-1)=231\), \(n-1=21\), and \(n=22\). Hence, the 22nd row has 252 plants. The 21st row would have only 241 plants. Exam tip: when a target term is given, equate it to \(a_n\) and solve for \(n\).
Frequently asked questions
What is the correct answer to this question?
22
Why is this the correct answer?
The numbers of plants form an arithmetic progression with first term \(a=21\) and common difference \(d=11\). The number of plants in the \(n\)th row is \(a_n=21+(n-1)\times 11\). Setting this equal to 252 gives \(21+(n-1)\times 11=252\), so \(11(n-1)=231\), \(n-1=21\), and \(n=22\). Hence, the 22nd row has 252 plants. The 21st row would have only 241 plants. Exam tip: when a target term is given, equate it to \(a_n\) and solve for \(n\).
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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