\[S_n = (n/2)*(2a_1 + (n-1)d)\]
Variables
Snsum of first n terms
nnumber of terms
a1first term
dcommon difference
Description
What is this formula?
This formula calculates the sum of the first n terms of an arithmetic progression.
When to use it
Use it when you need to compute cumulative totals of linearly increasing or decreasing sequences.
Example
Data:
a1 = 2, d = 3, n = 4
Formula:
Sn = (n/2)*(2a1 + (n-1)d)
Substitution:
S4 = (4/2)*(2*2 + (4-1)*3)
Result:
S4 = 26
Applications
Used in finance, physics, and discrete mathematics.