Formulas & tables/Mathematics/Sequences

Sequences

7 formulas · Mathematics

Arithmetic sequence — nth term
an=a1+(n−1)ra_n=a_1+(n-1)r
Sum of an arithmetic sequence
Sn=a1+an2⋅nS_n=\dfrac{a_1+a_n}{2}\cdot n
Middle term property (arithmetic)
an=an−1+an+12a_n=\dfrac{a_{n-1}+a_{n+1}}{2}
Geometric sequence — nth term
an=a1qn−1a_n=a_1 q^{n-1}
Sum of a geometric sequence
Sn=a11−qn1−qS_n=a_1\dfrac{1-q^{n}}{1-q}
Middle term property (geometric)
an2=an−1⋅an+1a_n^2=a_{n-1}\cdot a_{n+1}
Sum of a convergent geometric series
S=a11−qS=\dfrac{a_1}{1-q}