Arithmetic sequence — nth term

a_n=a_1+(n-1)r

Result unit: — (liczba)

What it describes

The nth term of an arithmetic sequence — to the first term we add the common difference (n−1) times.

a_n

nth term

a_1

first term

n

term index

r

common difference

Each successive term differs by a constant difference

r

. Instead of adding

r

step by step, we reach the nth term directly: the first term plus

(n-1)

differences.

Arithmetic sequences — when the increment is constant (rows in a theater, fixed installments).

For

a_1=3

r=2

compute

a_{10}

Substitution

a_1=3

r=2

n=10

Result

a_{10}=3+9\cdot2=21

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.