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Class 10MathematicsArithmetic Progressions (AP)Word problems based on APsExpert
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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 \(n\).

Related tags

Arithmetic ProgressionAp Word ProblemsNth TermLinear SequenceClass 10 MathematicsWord Problems Based On ApsArithmetic Progressions (Ap)Arithmetic Progressions Ap
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