NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.3 Question 14
NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.3 Question 14
Question:
Find the sum of the odd numbers between 0 and 50.
Given:
The range of numbers is between 0 and 50.
To Find:
The sum of odd numbers in the given range.
Formula:
The sum of an arithmetic series is given by: Sn = n 2 (a1 + an), where
n is the number of terms,
a1 is the first term, and
an is the last term.
Solution:
Odd numbers between 0 and 50 are 1, 3, 5, ..., 49.
To find the number of terms (n), we can use the formula for the nth term of an arithmetic sequence: an = a1 + (n-1)d, where
an = 49,
a1 = 1, and
d = 2.
⇒ 49 = 1 + (n-1)2
⇒ 48 = 2(n-1)
⇒ 24 = n-1
⇒ n = 25
Therefore, there are 25 odd numbers between 0 and 50.
Using the formula, sum of an arithmetic series given by: Sn = n 2 (a1 + an),
⇒ S25 = 25 2 ( 1 + 49 )
⇒ S25 = 25 x 50 2
⇒ S25 = 25 x 25
⇒ S25 = 625
Result:
The sum of odd numbers between 0 and 50 is 625.
Next question solution:
NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.3 Question 15
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