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

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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.

User Nikki Locke
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