Question

in a flower bed, there are 23 rose plant in the first row,21 in the second,19 in the third,and soon.There are 5 rose plants in the last row.How many rows are there in the flower bed?

Answer 1

First row= 23
Second row =21
Last row = 5
So as series is in the following way
23,21,.........................,5
a=23 D= -2 an= 5
an = a+(n-1)d. an = 23+(n - 1)-2
5-23 =(n-1)-2
-18 =(n-1)-2
-18/-2 =n-1
9 =n-1
9+1 =n
N =10

Answer 2

We have a1 = 23 , a2 =21 , a3= 19 and an = 5=l

Sn = ?

Now, an=a+(n-1)d

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

=> 5=23-2n+2

=> 5=25-2n

=> 2n=25-5

=> n=20/2

=> n=10

So, using Sn=n/2(a+l), we get

S10 = 10/2 ( 23+5 )

S10= 5 × 28 = 140

So, there are 140 rose plants in the flower bed.