Question

Find the sum of all integers between 50 and 500, which are divisible by 7.

Answer 1

Answer:

The sum of all integers between 50 and 500, which are divisible by 7 is 17696.

Step-by-step explanation:

Given :  

Integers between 50 and 500, which are divisible by 7  are 56, 63, 70,....... 497

Here,  

a = 56, d = 7, an(l) = 497

By using the formula ,an = a + (n - 1)d

497 = 56 + (n -1)7

497 - 56 =  7(n -1)

441 = 7(n -1)

n -1 = 441/7

n -1 = 63

n = 63 + 1  

n = 64

By using the formula ,Sum of nth terms , Sn = n/2 [a + l]

⇒ S64 = 64/2 (a + l)

⇒ S64 = 32 (56 + 497)

⇒ S64 = 32 (553)  

⇒ S64 = 17696

Hence, the sum of all integers between 50 and 500, which are divisible by 7 is 17696.

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Answer 2

Answer:

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