Sum of an arithmetic sequence

S_n=\dfrac{a_1+a_n}{2}\cdot n

Result unit: — (liczba)

What it describes

The sum of the first n terms of an arithmetic sequence.

S_n

sum of n terms

a_1

first term

a_n

nth term

n

number of terms

The sum is the average of the first and last term multiplied by their count — Gauss's trick (pairing terms from both ends).

Summing successive terms of an arithmetic sequence.

For

a_1=1

a_{10}=19

n=10

compute the sum.

Substitution

a_1=1

a_{10}=19

n=10

Result

S=\dfrac{1+19}{2}\cdot10=100

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.