Answer:
The series of integers divisible by 7 between 50 and 500 are 56, 63, 70, …, 497
Number of terms be ‘n’
a = 56, d = 63-56 = 7, an = 497
an = a + (n-1)d
497 = 56 + (n-1)7
497 = 56 + 7n – 7
7n = 497 – 56 + 7
7n = 448
n = 448/7
n = 64
By using the formula,
Sum of n terms,
S = n/2 [a + l]
S = 64/2 [56 + 497]
S = 32 [553]
S = 17696
∴ The sum of all integers between 50 and 500 which are divisible by 7 is 17696.