Question

In a flower garden, there are $23$ rose plants in the first row, $21$ in the second row, $19$ in the third row and so on. There are $5$ rose plants in the last row. How many rows are there in the flower garden?

Answer 1

Let $n$ be the number of rows in the flower garden.
The number of rose plants in the $1^{st},2^{nd},3^{rd},...,n^{th}$ rows are $23,21,19,...,5$ respectively.
Now, $t_k-t_{k-1}=-2$ for $k=2,...,n$.
Thus, the sequence $23,21,19,...,5$ is in an A.P.
We have $a=23,d=-2$ and $l=5$.
$\therefore n=\frac{l-a}{d}+\frac{5-23}{-2}+1=10$.
So, there are $10$ rows in the flower garden.