Geometric Sequences formula

Front

What is a geometric sequence?

Back

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Front

What is the formula for the nth term of a geometric sequence?

Back

Front

How do you find the common ratio in a geometric sequence?

Back

Front

Given the first term a1 = 3 and the common ratio r = 2, what is the 5th term of the geometric sequence?

Back

Front

What is the sum of the first n terms of a geometric sequence?

Back

Front

If the first term of a geometric sequence is 5 and the common ratio is 3, what is the 4th term?

Back

Front

What is the difference between an arithmetic sequence and a geometric sequence?

Back

An arithmetic sequence adds a constant value (common difference) to each term, while a geometric sequence multiplies by a constant value (common ratio).

Front

How can you determine if a sequence is geometric?

Back

Front

What is the explicit formula for the geometric sequence with a1 = 2 and r = 5?

Back

Front

If a geometric sequence has a common ratio of 1/2, what happens to the terms as n increases?

Back

The terms will decrease and approach zero as n increases, since each term is half of the previous term.