In a garden the first row has (25) plants and each next row has (8) more plants. Which row will have (153) plants?
Answer and explanation
Correct answer: 17
The numbers of plants form an arithmetic progression with first term 25 and common difference 8. Therefore, the number of plants in the nth row is \(a_n=25+(n-1)\times8\). Putting \(a_n=153\), we get \(25+(n-1)\times8=153\), so \(8(n-1)=128\) and hence \(n=17\). The 18th row would contain \(161\) plants, so it is not correct. Exam tip: equate the given target value to \(a_n\) and solve for \(n\).
Frequently asked questions
What is the correct answer to this question?
17
Why is this the correct answer?
The numbers of plants form an arithmetic progression with first term 25 and common difference 8. Therefore, the number of plants in the nth row is \(a_n=25+(n-1)\times8\). Putting \(a_n=153\), we get \(25+(n-1)\times8=153\), so \(8(n-1)=128\) and hence \(n=17\). The 18th row would contain \(161\) plants, so it is not correct. Exam tip: equate the given target value 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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