Question

in a flower bed there are hundred rose planets in the first row,97 in 2nd ,94 in 3rd and so on there are 10 Rose plants in the last row how many rows are there in the flower bed ​

Answer 1

Answer:

T1=100

T2=97

Tn=10

since it is in AP

Tn=a+(n-1)d=10

a=100,d=-3

10=100+(n-1)-3

10=100-3n+3

3n=113

n=37

Answer 2

Series is 100+97+94+........+10

Here, a=100, d =-3

Tn = a + (n-1)*d

or, 10 = 100+(n-1) *(-3)

10 = 100 -3n + 3

So, n = 31

Now, total no. of flowers = sum of the series

Sn = n/2(a + l)

= 31/2 (100+10)

=31/2(110)

=31*110/2

=55*31

=1705

Therefore total number of flowers is 1705.