Question

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

Answer 1

Answer:

There are 10 rows.

Step-by-step explanation:

AP : 23 + 21 + 19 +.........+5

a = 23 ;  l = 5 ; d = -2

l = a +  (n-1) * d

5 =  23 + (n-1) * (-2)

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

-18 = (n-1) * (-2)

(-18) / (-2) = n-1

9 = n-1

n = 9 + 1 =10

Answer 2

Answer:

23, 21, 19,. ........, 5 is an A. P.

a=t1=23, d=21-23=-2, tn=5

We find number of rows

i. e. n=?

tn=a+(n-1)×d ... (formula)

5=23+(n-1)×(-2)

5=23-2n+2

5=25-2n

5-25=-2n

-20=-2n

-20÷(-2)=n

n=10

Numbers of rows is 10.

Now, we find total numbers of rose plants

i. e. Sn=?

Sn=n÷2(t1+tn)

Sn=10÷2(23+5)

Sn=5×28

Sn=140

There are total number of rose plants is 140

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