\[a_n = a_1 + (n-1)d : S_n = \frac{n}{2}(a_1 + a_n)\]
Variables
annth term
a1first term
nnumber of terms
dcommon difference
Snsum of first n terms
Description
What is this formula?
This set of formulas describes both the general term and the sum of an arithmetic progression.
When to use it
Use it when dealing with linear sequences and cumulative sums.
Example
Data:
a1 = 2, d = 3, n = 5
Step 1:
an = a1 + (n-1)d → a5 = 2 + 4*3 = 14
Step 2:
Sn = (n/2)(a1 + an) → S5 = (5/2)(2 + 14)
Result:
S5 = 40
Applications
Used in finance, physics, and sequence modeling.