Question

Savita planted 23 rose plants in the first row flower by 21 plants and 2nd 19 in the third and so on

Answer 1

Correct Que:-

In a garden bed, there are 23 rose plants in the first row, 21 are in the 2nd, 19 in 3rd row and so on. There are 5 plants in the last row. How many rows are there of rose plants ? Also find the total number of rose plants in the garden.

Solution:-

Given A.P :-

• 23 , 21 , 19 , 17 , ............ , 5.
• First Term (a) = 23
• Common Difference (d)= 21 - 23 = -2
• Last term ( an) = 5

To Find:-

• Total rows of Rose plant = ?
• Total Number of Rose plants = ?

Find:-

an = a + ( n - 1)d

=) 5 = 23 + ( n - 1)(-2)

=) 5 - 23 = ( n - 1)(-2)

=) -18/-2 = n - 1

=) n - 1 = 9

=) n = 10.

Hence,

• There are 10 rows of rose plant.

Now,

Sn = n/2 [ 2a + ( n -1)d ]

=) S10 = 10/2 [ 2 × 23 + ( 10 - 1)(-2) ]

=) S10 = 5 [ 46 + 9(-2) ]

=) S10 = 5[ 46 - 18 ]

=) S10 = 5 × 28

=) S10 = 140

Hence,

• There are total 140 rose plants.