Geometric sequence — nth term

a_n=a_1 q^{n-1}

Result unit: — (liczba)

What it describes

The nth term of a geometric sequence — the first term multiplied (n−1) times by the common ratio.

a_n

nth term

a_1

first term

q

common ratio

n

term index

Each term is the previous one multiplied by the common ratio

q

. We reach the nth term by multiplying the first by

q^{n-1}

Geometric sequences — percentage growth, compound interest, decay.

For

a_1=2

q=3

compute

a_4

Substitution

a_1=2

q=3

n=4

Result

a_4=2\cdot3^3=54

Found this formula useful? Share it.

It's free — send it to a friend who's revising.

Teaching? Embed this formula on your site.

Free widget — paste it on your school site, blog or notes. It links to the full version.