Answer:
The sum of all integers which are divisible by 6 lie between 1 and 1000 is 83,166
Explanation:
The numbers divisible by 6 and between 1 and 1,000 are given as follows;
6, 12, ... , 996
Therefore, the numbers form an arithmetic progression with first term, a = 6 the common difference, d = 6 and the number of terms, n = 166
The sum, Sₙ, of an arithmetic progression, AP, is given as follows;
Sₙ = n/2 × (2·a + (n - 1)·d)
Substituting the known values for the arithmetic progression formed by the numbers divisible by 6 and lie between 1 and 1,000 gives the sum of all integers which are divisible by 6 lie between 1 and 1000;
Sₙ = 166/2 × (2 × 6 + (166 - 1) × 6) = 83,166
Therefore, the sum of all integers which are divisible by 6 lie between 1 and 1000 = 83,166.
