NCERT Class X Chapter 5: Arithmetic Progression Example 10
NCERT Class X Chapter 5: Arithmetic Progression Example 10
Question:
In a flower bed, there are 23 rose plants in the first row, 21 in the second, 19 in the third, and so on. There are 5 rose plants in the last row. How many rows are there in the flower bed?.
Given:
Number of rose plants in the first row = 23
Number of rose plants in the second row = 21
Number of rose plants in the third row = 19
Number of rose plants in the last row = 5
To Find:
The number of rows in the flower bed.
Formula:
The number of terms (n) in an arithmetic progression can be found using the formula:
l = a + (n - 1)d
where:
l = last term
a = first term
n = number of terms
d = common difference
Solution:
This is an arithmetic progression with
first term (a) = 23,
last term (l) = 5, and
common difference (d) = -2.
Using the formula l = a + (n - 1)d we have
5 = 23 + (n - 1)(-2)
⇒ 5 = 23 - 2n + 2
Grouping terms on both side we have,
⇒ 2n = 23 + 2 - 5
⇒ 2n = 20
⇒ n = 20 2 = 10
Result:
Therefore, there are 10 rows in the flower bed.
Next question solution
NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.2 Question 1(i)
Thank you!
ReplyDeleteVery insightful.