Question

Find the sum of all the first n odd natural numbers 2. find the sum of all natural numbers between 1 and 201 which are divisible by 5 3. find the first four terms of a sequence of which sum to n terms is 1/2 n (7n-1)

Answer 1

Sum of numbers up to 1000 = (1/2)*1000*1001 = 500500 
Sum of numbers divisible by 2 up to 1000 = 2*(1+2+...500) = 2*(1/2)*500*501 = 250500 
Sum of numbers divisible by 5 up to 1000 = 5*(1+2+...200) = 5*(1/2)*200*201 = 100500 
Sum of numbers divisible by both 2 and 5 up to 1000 = 10*(1+2+3+...100) = 10*(1/2)*100*101 = 50500 
Required sum = 500500 - 250500 - 100500 + 50500 = 200000