Question

In a flower bed, 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 bed?

Answer 1

The rose plants in rows are in AP where,

$t_1=a=23,t_2=21,t_3=19,t_n=5$

$d=t_2-t_1=21-23=-2$

Now, $t_n=a+(n-1)\times d$

or, $5=23+(n-1)\times (-2)$

or, $-18=(n-1)\times (-2)$

or, $n-1=9$

or, $n=10$