Question

3.
3
Add all integers divisible by 7 lying between
56 and 1000. 994​

Answer 1

Given:

The range of integers on which the operation is to be performed= 56 to 1000

To find:

Sum of all the integers divisible by 7.

Solution:

Since the first integer divisible by 7 after 56 is 63 and the last integer to be divisible by 7 before 1000 is 994.

The sum in an arithmetic progression:

n/2 (2a + (n-1)d)

The formula for nth term in an arithmetic progression is:

an = a1 + (n-1)d

994 = 56 + (n-1)7

938 = (n-1)7

n = 135

Sum = 135/2 (112 + 134*7)

= 70,875

Therefore the sum of integers divisible by 7 lying between 56 and 1000 is 70,875.