# Arithmetic progression Calculator

## Calculates the n-th term and sum of the arithmetic progression with the common difference.

 $\normal Sn=a+(a+d)+(a+2d)+\cdots +(a+(n-1)d)\\$
initial term a
common difference d
number of terms n
 n＝1,2,3...

the n-th term an
sum Sn
 $\normal Arithmetic\ progression\\\vspace{5}(1)\ a_n=a+(n-1)d\\(2)\ Sn={\large\sum_{\small k=1}^{\small n}}a_k\\\hspace{30} =a+(a+d)+(a+2d)+\cdots +(a+(n-1)d)\\\hspace{30} ={\large\frac{n}{2}}(a+a_n)\\\hspace{30} ={\large\frac{n}{2}}(2a+(n-1)d)\\$

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