Question

In flower bed, there are $23$ rose plants in the first row, twenty-one in the second row, nineteen in the third row and so on. There are five plants in the last row. How many rows are there in the flower bed?

Answer 1

The number of rose plants in first, second third,..., and last row are respectively.
$23,21,19,....,5$.

Let the number of rows of rose plants $n$.
The sequence $23,21,19,....,5$ is an A.P. with first term $a(=23)$, common difference $d(=-2)$ and $n^{th}$ term $(=5)$.
$\therefore a_n=a+(n-1)d$
$⟹5=23+(n-1)\times -2$
$⟹5=23-2n+2⟹20=2n⟹n=10$

Hence, there are $10$ rows of rose plants.