In a garden the first row has (16) plants and each next row has (6) more plants. Which row will have (112) plants?
Answer and explanation
Correct answer: 17
The numbers of plants form an arithmetic progression with first term 16 and common difference 6. Thus, the number of plants in the nth row is \(a_n=16+(n-1)\times6\). On putting \(16+(n-1)\times6=112\), we get \(n-1=16\), so \(n=17\). Therefore, the 17th row has 112 plants. The 16th row would have only 106 plants. Exam tip: in AP word problems, identify the first term and common difference, then equate the target value to \(a_n\).
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 16 and common difference 6. Thus, the number of plants in the nth row is \(a_n=16+(n-1)\times6\). On putting \(16+(n-1)\times6=112\), we get \(n-1=16\), so \(n=17\). Therefore, the 17th row has 112 plants. The 16th row would have only 106 plants. Exam tip: in AP word problems, identify the first term and common difference, then equate the target value to \(a_n\).
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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