Sum of a geometric sequence

S_n=a_1\dfrac{1-q^{n}}{1-q}

Result unit: — (liczba)

What it describes

The sum of the first n terms of a geometric sequence (for

q\neq 1

S_n

sum of n terms

a_1

first term

q

common ratio (

q\neq 1

)

n

number of terms

A compact formula for the sum of the terms of a geometric sequence (for

q\neq1

). When

q=1

, all terms are equal, so

S=n\cdot a_1

Summing a geometric sequence (sum of installments, repayments).

For

a_1=1

q=2

n=5

compute the sum.

Substitution

a_1=1

q=2

n=5

Result

S=1\cdot\dfrac{1-32}{1-2}=31

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