in a flower bed there are 23 Rose plants in the first row 25 on the second 27 in the third row so on. there are 97 rose in the last row. how many rows are there in flower bed.
Answers
AP = 23,21,19....,5
a = 23
an=5
d = 32-21= 2
n = no of rows
now an = a+ (n-1)d
5 = 23 + (n-1) 2
-18/2 = n-1
8 =n
Step-by-step explanation:
Given :-
In a flower bed there are 23 Rose plants in the first row 25 on the second 27 in the third row so on. there are 97 rose in the last row.
To find :-
How many rows are there in flower bed?
Solution :-
Given that
Number of rose plants in the first row in a flower bed = 23
Number of rose plants in the second row in the flower bed = 25
Number of rose plants in the third row in the flower bed = 27
Number of rose plants in the last row in the flower bed = 97
This is an daily life situation related to Arithmetic Progression.
We have
First term(a) = 23
Second term (a2) = 25
Third term (a3) = 27
Last term (l) = 97
The Arithmetic Progression is 23,25,27,...,97
Common difference = a2-a1 = 25-23 = 2
d = 2
Let the nth term of the AP = 97
We know that
The general term of the AP = an = a+(n-1)d
=> an = 97
=> a+(n-1)d = 97
On Substituting the values of a and d in the formula then
=> 23+(n-1)(2) = 97
=> 23 +2n -2 = 97
=> 21+2n = 97
=> 2n = 97-21
=> 2n = 76
=> n = 76/2
=> n = 38
Therefore, number of rows = 38
Answer:-
The total number of rows in the given flower bed is 38
Check :-
The Arithmetic Progression is 23,25,27,...
an = a+(n-1)d
a38 = 23+(38-1)(2)
=> a38 = 23+(37)(2)
=> a38 = 23+74
=> a38 = 97
Verified the given relations in the given problem
Used formulae:-
The general term of the AP = an = a+(n-1)d
- a = First term
- d = Common difference
- n = number of terms