In a flower bed there are 23 rose plants in the first row, 21 in the second, 19 in the third and so on. There are 5 rose plants in the last row. Then the number of rows in the flower bed is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 10
The rows 23, 21, 19, … go down by the same number each time, so they form an arithmetic progression (AP). The \(n\)th term of an AP is \(a_n=a+(n-1)d\), where \(a\) is the first term and \(d\) the common difference; the number of rows is the value of \(n\) for which the term is 5.
First row \(a=23\); each row has 2 plants fewer, so \(d=21-23=-2\)
The last row has 5 plants: \(5=23+(n-1)(-2)\)
The drop from 23 to 5 is 18 plants, made in steps of 2: \(2(n-1)=18\), so \(n-1=9\) steps after the first row
Number of rows \(n=9+1=10\)