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(D) The number of rose plants in the $1^{st}, 2^{nd}, 3^{rd}, \dots$ rows are $23, 21, 19, \dots, 5$.This sequence forms an Arithmetic Progression $(A

Vedclass · Accepted Answer

$10$

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(D) The number of rose plants in the $1^{st}, 2^{nd}, 3^{rd}, \dots$ rows are $23, 21, 19, \dots, 5$.This sequence forms an Arithmetic Progression $(AP)$ because the difference between consecutive terms is constant.Here,the first term $a = 23$ and the common difference $d = 21 - 23 = -2$.The last term (or $n^{th}$ term) is $a_n = 5$.Using the formula for the $n^{th}$ term of an $AP$: $a_n = a + (n - 1)d$.Substituting the values: $5 = 23 + (n - 1)(-2)$.Subtracting $23$ from both sides: $5 - 23 = (n - 1)(-2) \implies -18 = (n - 1)(-2)$.Dividing by $-2$: $9 = n - 1$.Therefore,$n = 10$.There are $10$ rows in the flower bed.

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. How many rows are there in the flower bed?

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