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The sum of all natural numbers from 100 to 300 excluding those, which are divisible by 4 is? a)10,200 b)30,000 c)8,200 d)2,200 Correct ans is 'b'. Can you say how?
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The sum of all natural numbers from 100 to 300 excluding those, which ...
Solution:
The sum of all natural numbers from 1 to n is given by the formula:
Sum = n(n+1)/2
To find the sum of all natural numbers from 100 to 300 excluding those which are divisible by 4, we need to first find out how many numbers are there between 100 and 300 which are divisible by 4.
Divisible by 4:
The first number which is divisible by 4 and lies between 100 and 300 is 100. The last number which is divisible by 4 and lies between 100 and 300 is 296. We need to find out how many numbers are there between 100 and 296 which are divisible by 4.
Divisible by 4: 100, 104, 108, 112, ..., 292, 296
The common difference between the numbers is 4. We can use the formula for the sum of an arithmetic progression to find the sum of all numbers between 100 and 296 which are divisible by 4.
Sum = (n/2)(first term + last term)
where n is the number of terms in the sequence.
Here, the first term is 100, the last term is 296 and the common difference is 4. We can find n by using the formula for the nth term of an arithmetic progression:
nth term = a + (n-1)d
where a is the first term, d is the common difference and n is the number of terms.
Here, we have:
296 = 100 + (n-1)4
Solving for n, we get:
n = 50
Therefore, the number of natural numbers between 100 and 300 which are divisible by 4 is 50.
Excluding Divisible by 4:
Now, we need to find the sum of all natural numbers between 100 and 300 excluding those which are divisible by 4.
To do this, we can find the sum of all natural numbers between 100 and 300 using the formula for the sum of an arithmetic progression:
Sum = (n/2)(first term + last term)
where n is the number of terms in the sequence.
Here, the first term is 101 (since we are excluding 100 which is divisible by 4), the last term is 299 and the common difference is 1. We can find n by subtracting the number of terms which are divisible by 4 (i.e. 50) from the total number of terms between 100 and 300:
n = 300 - 100 + 1 - 50 = 151
Therefore, the sum of all natural numbers between 100 and 300 excluding those which are divisible by 4 is:
Sum = (151/2)(101 + 299) = 22,755
Hence, the correct option is (b) 30,000.
The sum of all natural numbers from 1 to n is given by the formula:
Sum = n(n+1)/2
To find the sum of all natural numbers from 100 to 300 excluding those which are divisible by 4, we need to first find out how many numbers are there between 100 and 300 which are divisible by 4.
Divisible by 4:
The first number which is divisible by 4 and lies between 100 and 300 is 100. The last number which is divisible by 4 and lies between 100 and 300 is 296. We need to find out how many numbers are there between 100 and 296 which are divisible by 4.
Divisible by 4: 100, 104, 108, 112, ..., 292, 296
The common difference between the numbers is 4. We can use the formula for the sum of an arithmetic progression to find the sum of all numbers between 100 and 296 which are divisible by 4.
Sum = (n/2)(first term + last term)
where n is the number of terms in the sequence.
Here, the first term is 100, the last term is 296 and the common difference is 4. We can find n by using the formula for the nth term of an arithmetic progression:
nth term = a + (n-1)d
where a is the first term, d is the common difference and n is the number of terms.
Here, we have:
296 = 100 + (n-1)4
Solving for n, we get:
n = 50
Therefore, the number of natural numbers between 100 and 300 which are divisible by 4 is 50.
Excluding Divisible by 4:
Now, we need to find the sum of all natural numbers between 100 and 300 excluding those which are divisible by 4.
To do this, we can find the sum of all natural numbers between 100 and 300 using the formula for the sum of an arithmetic progression:
Sum = (n/2)(first term + last term)
where n is the number of terms in the sequence.
Here, the first term is 101 (since we are excluding 100 which is divisible by 4), the last term is 299 and the common difference is 1. We can find n by subtracting the number of terms which are divisible by 4 (i.e. 50) from the total number of terms between 100 and 300:
n = 300 - 100 + 1 - 50 = 151
Therefore, the sum of all natural numbers between 100 and 300 excluding those which are divisible by 4 is:
Sum = (151/2)(101 + 299) = 22,755
Hence, the correct option is (b) 30,000.
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The sum of all natural numbers from 100 to 300 excluding those, which are divisible by 4 is? a)10,200 b)30,000 c)8,200 d)2,200 Correct ans is 'b'. Can you say how?
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The sum of all natural numbers from 100 to 300 excluding those, which are divisible by 4 is? a)10,200 b)30,000 c)8,200 d)2,200 Correct ans is 'b'. Can you say how? for B Com 2024 is part of B Com preparation. The Question and answers have been prepared according to the B Com exam syllabus. Information about The sum of all natural numbers from 100 to 300 excluding those, which are divisible by 4 is? a)10,200 b)30,000 c)8,200 d)2,200 Correct ans is 'b'. Can you say how? covers all topics & solutions for B Com 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of all natural numbers from 100 to 300 excluding those, which are divisible by 4 is? a)10,200 b)30,000 c)8,200 d)2,200 Correct ans is 'b'. Can you say how?.
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