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The sum of the first 100 numbers, 1 to 100 is divisible by
- a)1,2,4,8
- b)2 and 4
- c)2
- d)none
Correct answer is option 'C'. Can you explain this answer?
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The sum of the first 100 numbers, 1 to 100 is divisible bya)1,2,4,8b)2...
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The sum of the first 100 numbers, 1 to 100 is divisible bya)1,2,4,8b)2...
The sum of the first 100 numbers, 1 to 100, can be calculated using the formula for the sum of an arithmetic series. The formula is given by:
S = (n/2)(a + l)
where S is the sum of the series, n is the number of terms, a is the first term, and l is the last term.
In this case, we have n = 100, a = 1, and l = 100. Plugging these values into the formula, we get:
S = (100/2)(1 + 100)
S = 50(101)
S = 5050
Therefore, the sum of the first 100 numbers is 5050.
To determine which options this sum is divisible by, we can perform the division:
5050 ÷ 1 = 5050
5050 ÷ 2 = 2525
5050 ÷ 4 = 1262.5
5050 ÷ 8 = 631.25
Therefore, the sum of the first 100 numbers is divisible by 1, 2, and 4.
Now, let's analyze the given options:
a) 1, 2, 4, 8: This option is incorrect because the sum of the first 100 numbers is not divisible by 8.
b) 2 and 4: This option is incorrect because the sum of the first 100 numbers is divisible by 1 and 4, but not just by 2.
c) 2: This option is correct because the sum of the first 100 numbers is divisible by 2.
d) None: This option is incorrect because the sum of the first 100 numbers is divisible by 2.
Therefore, the correct answer is option 'C', which states that the sum of the first 100 numbers is divisible by 2.
S = (n/2)(a + l)
where S is the sum of the series, n is the number of terms, a is the first term, and l is the last term.
In this case, we have n = 100, a = 1, and l = 100. Plugging these values into the formula, we get:
S = (100/2)(1 + 100)
S = 50(101)
S = 5050
Therefore, the sum of the first 100 numbers is 5050.
To determine which options this sum is divisible by, we can perform the division:
5050 ÷ 1 = 5050
5050 ÷ 2 = 2525
5050 ÷ 4 = 1262.5
5050 ÷ 8 = 631.25
Therefore, the sum of the first 100 numbers is divisible by 1, 2, and 4.
Now, let's analyze the given options:
a) 1, 2, 4, 8: This option is incorrect because the sum of the first 100 numbers is not divisible by 8.
b) 2 and 4: This option is incorrect because the sum of the first 100 numbers is divisible by 1 and 4, but not just by 2.
c) 2: This option is correct because the sum of the first 100 numbers is divisible by 2.
d) None: This option is incorrect because the sum of the first 100 numbers is divisible by 2.
Therefore, the correct answer is option 'C', which states that the sum of the first 100 numbers is divisible by 2.
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Community Answer
The sum of the first 100 numbers, 1 to 100 is divisible bya)1,2,4,8b)2...
N(n+1)/2 =100(100+1)/2
100(101)/2
= 50(101)
= 101 is a odd number
= 50 is divided by 2 so
answer is 2
100(101)/2
= 50(101)
= 101 is a odd number
= 50 is divided by 2 so
answer is 2
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The sum of the first 100 numbers, 1 to 100 is divisible bya)1,2,4,8b)2 and 4c)2d)noneCorrect answer is option 'C'. Can you explain this answer?
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