Geometric Sequence & Series

Vocabulary flashcards on geometric sequence definitions, common ratio, nth term formula, and geometric series formulas.

Geometric Sequence

A sequence in which each term is obtained by multiplying the previous term by a fixed non-zero number.

Common Ratio ($r$)

The fixed non-zero number used to multiply a term in a sequence to obtain the next term, defined as the ratio of any two consecutive terms: $r = \frac{a_{n+1}}{a_n}$.

Formula for the Nth Term of a Geometric Sequence

The algebraic formula used to find the value of any term at position $n$, given by $a_n = a_1 r^{n-1}$.

Geometric Series

The sum of the terms of a geometric sequence.

Finite Geometric Series Formula

The formula used to calculate the sum of a specific number of terms $n$ in a geometric sequence, given by $S_n = \frac{a_1(1 - r^n)}{1 - r}$.

Infinite Geometric Series Formula

The formula used to calculate the sum of an infinite geometric series, given by $S_n = \frac{a_1}{1 - r}$.

First Term ($a_1$)

The symbol representing the initial term in a geometric sequence or series formula.

Nth Term ($a_n$)

The symbol representing the value of the term located at position $n$ in a geometric sequence.

Position / Number of Terms ($n$)

The symbol representing the numerical position of a term or the total count of terms in geometric sequence and series formulas.

Sum of Terms ($S_n$)

The symbol representing the total sum of $n$ terms in a geometric series.

Steps to Find the Nth Term

1. Identify the first term ($a_1$). 2. Determine the common ratio ($r$). 3. Identify the value of $n$. 4. Substitute the values into the formula $a_n = a_1 r^{n-1}$. 5. Solve.