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WOLFRAM|DEMONSTRATIONS PROJECT

Sum of an Arithmetic Progression

​
first term a
last term z
number of terms n
1 + 2 + 3 + … + 100
+
100 + 99 + 98 + … + 1
=
101 + 101 + 101 + … + 101
Therefore
1 + 2 + 3 + … + 100
=
101 ×
100
2
= 5050

This Demonstration lets you explore the sum of an arithmetic progression with first term
a
, last term
z
, and number of terms
n
.

In general, the sum of such an arithmetic progression is
n
2
(a+z)
.