Arithmetic Progression Explicit Term Formulas
Arithmetic Progression Explicit Term Formulas
\[a_n = a_1 + (n-1)d : S_n = \frac{n}{2}(a_1 + a_n)\]
Variables
an = nth term
a1 = first term
n = number of terms
d = common difference
Sn = sum 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.
Download the fCalc app to calculate this formula and thousands more:
