Question

How many integers between 50 and 5000 are divisible 7?explain full ​

Answer 1

• There are 448 numbers between 50 and 500 which is divisible by 7 . The first one is 56 and the last is 497 . So if there are 448 numbers and every seventh one is divisible by 7 , 448/ 7 = 64 . So , there are 64 numbers between 50 and 500 are divisible by 7 .

Answer 2

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➤ The required A.P is

56, 63, 70,.........., 497

⇉ a = 56

⇉ d = T2 - T1

⇉ d = 63 - 56

⇉ d = 7

⇉ Tn = a +(n-1)d

⇉ 497 = 56 + (n-1)7

⇉ 497-56 = (n-1)7

⇉ 441/7 = n-1

⇉ 63 +1 = n

⇉ n = 64 terms

➤ Sn = n/2 (a+l)

⇉ S 64 = 64/2 ( 56 + 497)

⇉ S 64 = 32 x 553

⇉ S 64 = 17,696

➤ Hence the sum of all integers between 50 and 500 divisible by 7 is 17,696

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