Arithmetic Progression General Term Formula
Arithmetic Progression General Term Formula
\[a_n = a_1 + (n-1)d\]
Variables
an = nth term of the sequence
a1 = first term
n = term index
d = common difference
Description
What is this formula?
This formula calculates the nth term of an arithmetic progression using a linear relationship.
When to use it
Use it when you need to find any term in a sequence with constant difference between terms.
Example
Data:
a1 = 3, d = 2, n = 5
Formula:
an = a1 + (n-1)d
Substitution:
a5 = 3 + (5-1)*2
Result:
a5 = 11
Applications
Used in sequences, financial modeling, and discrete mathematics.
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