Math, asked by soujanya7122, 11 months ago

Find the sum of integers from 1 to 100 which are divisible by 2 or 5.​

Answers

Answered by selvisundramony
1

Answer:

2,4,6,8......100

Step-by-step explanation:

check the google

Answered by Anonymous
75

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The integers from 1 to 100, which are divisible by 2, are 2, 4, 6 ….. 100

This forms an A.P. with both the first term and common difference equal to 2.

 \tt  ⇒ 100=2+(n-1)2

 \tt  ⇒ n= 50

Therefore, the sum of integers from 1 to 100 that are divisible by 2 is given as:

 \tt  2+4+6+…+100 = (50/2)[2(2)+(50-1)(2)]

 \tt  = (50/2)(4+98)

 \tt  = 25(102)

 \tt  = 2550

The integers from 1 to 100, which are divisible by 5, 10…. 100

This forms an A.P. with both the first term and common difference equal to 5.

Therefore, 100= 5+(n-1)5

 \tt  ⇒5n = 100

 \tt  ⇒ n= 100/5

 \tt  ⇒ n= 20

Therefore, the sum of integers from 1 to 100 that are divisible by 2 is given as:

 \tt  5+10+15+…+100= (20/2)[2(5)+(20-1)(5)]

 \tt  = (20/2)(10+95)

 \tt  = 10(105)

 \tt  = 1050

Hence, the integers from 1 to 100, which are divisible by both 2 and 5 are 10, 20, ….. 100.

This also forms an A.P. with both the first term and common difference equal to 10.

Therefore, 100= 10+(n-1)10

 \tt  ⇒10n = 100

 \tt  ⇒ n= 100/10

 \tt  ⇒ n= 10

 \tt  10+20+…+100= (10/2)[2(10)+(10-1)(10)]

 \tt  = (10/2)(20+90)

 \tt  = 5(110)

 \tt  = 550

Therefore, the required sum is:

 \tt  = 2550+ 1050 – 550

 \tt  = 3050

Hence, the sum of the integers from 1 to 100, which are divisible by 2 or 5 is 3050

Hope it's Helpful.....:)

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