Question

In a flower bed, there are 25 rose plants in the first

row, 23 in the second, 21 in the third and so on.

There are 3 rose plants in the last row.

(i) How many rows are there in the flower bed?



(ii) Find the total number of rose plants in the

flower bed. ​

Answer 1

Answer:

rows of flower bed=12

total no. or roses=168

Answer 2

$Number \:of \: rose \:plants \: in \:the \: first$

$row (a= a_{1}) = 25$

$Number \:of \: rose \:plants \: in \:the$

$Second \:row (a_{2}) = 23$

$Number \:of \: rose \:plants \: in \:the$

$Third \:row (a_{3}) = 21$

$Number \:of \: rose \:plants \: in \:the$

$last \:row (a_{n}) = 3$

$Here, First \:term (a = a_{1}) = 25$

$Common \: difference (d)$

$= a_{2} - a_{1}$

$= 23 - 25$

$= -2$

/* We know that */

$a_{n} = a + (n-1)d$

$\implies 3 = 25 + (n-1)(-2)$

$\implies 3 - 25 = (n-1)(-2)$

$\implies -22 = (n-1) (-2)$

$\implies 11 = n - 1$

$\implies 11 + 1 = n$

$\red{ Number \: of \: rows \:in \: the \: flower \:bed}$

$n = 12$

$Total \: number \: of \: flower \: plants \: in$

$n \: rows (S_{n}) = \frac{n}{2}[a + a_{n}]$

$S_{12} = \frac{12}{2}(25 + 3 )$

$= 6 \times 28$

$= 168$

Therefore.,

$\red{ Total \: number \: of \: flower \: plants \: in}$

$\red{12 \: rows} \green { = 168}$

•••♪