D) 8,1030.The sum of integers from 1 to 100 that are divisible by 2 (o

1.	D) 8,1030.The sum of integers from 1 to 100 that are divisible by 2 (or) 5 is[IITJEE-IC) 5030D) 7030B) 3070A) 3050
Answer» 1 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. ⇒100 = 2 + (n–1) 2 ⇒n= 50 2 The integers from 1 to 100, which are divisible by 5, are 5, 10… 100. This forms an A.P. with both the first term and common difference equal to 5. ∴100 = 5 + (n–1) 5 ⇒ 5n= 100 ⇒n= 20 3 The integers, 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. ∴100 = 10 + (n–1) (10) ⇒ 100 = 10n ⇒n= 10 4 ∴Required sum = 2550 + 1050 – 550 = 3050 Thus, the sum of the integers from 1 to 100, which are divisible by 2 or 5, is 3050.

D) 8,1030.The sum of integers from 1 to 100 that are divisible by 2 (or) 5 is[IITJEE-IC) 5030D) 7030B) 3070A) 3050

Answer»

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.

⇒100 = 2 + (n–1) 2

⇒n= 50

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

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

∴100 = 5 + (n–1) 5

⇒ 5n= 100

⇒n= 20

The integers, 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.

∴100 = 10 + (n–1) (10)

⇒ 100 = 10n

⇒n= 10

∴Required sum = 2550 + 1050 – 550 = 3050

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