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The sum of all the integers from 1 to 100 which are divisible

Question

The sum of all the integers from $1$ to $100$ which are divisible by $2$ or $5$ is

3000

3050

3600

3250

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The sum of all the integers from

1

100

which are divisible by

2

5

12 mins ago

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Text solutionVerified

The A.P of the numbers divisible by

2

between

1

and

100

2, 4.......100

Therefore,

a = 2

and

a_{n} = 100

n = \frac{a _{n} - a}{d} + 1

= \frac{100 - 2}{2} + 1

= 50

Hence,

S_{n} = \frac{n}{2} (a + a_{n})

= \frac{50}{2} (102)

= 50 (51)

= 2550

........(i)

The A.P of the numbers divisible by

5

between

1

and

100

5, 10..100

n = \frac{a _{n} - a}{d} + 1

= \frac{100 - 5}{5} + 1

= 20

Hence,

S_{n} = \frac{20}{2} 105

= 10 (105)

= 1050

.......(ii)

The A.P of the numbers divisible by both

2

and

5

both is

10, 20..100

Therefore,

n = 10

S_{n} = 10 (\frac{110}{2})

= 550

.......(iii)

Hence, the required sum is

2550 + 1050 - 550

= 3600 - 550

= 3050

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Question Text	The sum of all the integers from $1$ to $100$ which are divisible by $2$ or $5$ is
Answer Type	Text solution:1
Upvotes	150

The sum of all the integers from 1 to 100 which are divisible by 2 or 5 is

Text solutionVerified

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