In a garden the first row has (18) plants and each next row has (9) more plants. Which row will have (207) plants?
Answer and explanation
Correct answer: 22
This forms an arithmetic progression with first term \(a=18\) and common difference \(d=9\). The number of plants in the \(n\)th row is \(a_n=18+(n-1)\times 9\). Putting \(a_n=207\), \(18+(n-1)\times 9=207\). Thus, \((n-1)\times 9=189\), so \(n-1=21\) and \(n=22\). Hence, the 22nd row has 207 plants. The 23rd row would have 216 plants, so it is not correct. Exam tip: equate the target quantity directly 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?
This forms an arithmetic progression with first term \(a=18\) and common difference \(d=9\). The number of plants in the \(n\)th row is \(a_n=18+(n-1)\times 9\). Putting \(a_n=207\), \(18+(n-1)\times 9=207\). Thus, \((n-1)\times 9=189\), so \(n-1=21\) and \(n=22\). Hence, the 22nd row has 207 plants. The 23rd row would have 216 plants, so it is not correct. Exam tip: equate the target quantity directly 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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