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Arithmetic progression. Formula for the nth term and the sum of the first n terms

Definition
An arithmetic progression is a sequence where each next term is obtained from the previous one by adding the same number dd (the common difference). Recursively: an+1=an+da_{n+1}=a_n+d. If d>0d>0 the terms grow; if d<0d<0 they decrease; if d=0d=0 all terms equal a1a_1.
Any two neighbours differ by dd: an+1an=da_{n+1}-a_n=d
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