Question

In a garden 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 of rose plants?

• A. $12$ rows
• B. $10$ rows
• C. $14$ rows
• D. $16$ rows

Answer 1

Answer: (B)

$10$ rows

Clearly, rose plants in the rows from an AP $23,21,19,...,5$ with first term $a=23$ and common difference $d=-2$.
Let there be $n$ rows. Then,
$a_n=5\Rightarrow a+(n-1)d$

$5=23+(n-1)\times -2$
$\therefore n=10$
Therefore, there are $10$ rows of rose plants.