Question

find the difference between the sum of the first 900 multiples of three and the sum pf the first 900 multiples of four

Answer 1

We have to find the sum of first 900 multiples of three and then sume of first 900 multiples of four.

1. Sum of first 900 multiples of three

i.e, 3, 6,9,12,.......3X900

This is in Arithmetic series,

first term, a = 3, common difference d = 3, last term (l) = 2700 and no.of terms n = 900

Sum of the n terms in arithmetic series =

substituting the values, we get

= 1216350

2.

Sum of first 900 multiples of four

i.e,4,8,12,16........4X900

This is in Arithmetic series,

first term, a = 4, common difference d = 4, last term (l) = 3600 and no.of terms n = 900

Sum of the n terms in arithmetic series =

substituting the values, we get

= 1621800

Now, the difference is

1621800-1216350

= 405450 is the required answer.