Question

302 + 299 + 296 + 293 ... + 2 = _____ what is the sequence using Gauss’s Law

Answer 1

By Gauss's Law the approach of solving sum of a sequence of n terms in arithmetic progression is :

`S_n=(n)/(2)(a_1+a_n)` ......1 )

Here,
`a_n = 302` ,
`a_1=2` .

We know :

`a_n=a_1+(n-1)d\\\\302=2+3(n-1)\\\\n = 101`

Putting, all values in equation 1) we get :

`S_n=(101)/(2)* (2+302)\\\\S_n=101* 152\\\\S_n=15352`

Therefore, the sum of sequence using Gauss's Law is 15352.

Hence, this is the required solution.