Arithmetic and Geometric Sequences Review

Front

What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is called the common difference (d).

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 (r).

Front

How do you find the common difference in an arithmetic sequence?

Back

The common difference (d) can be found by subtracting any term from the subsequent term: d = a_{n+1} - a_n.

Front

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

Back

The common ratio (r) can be found by dividing any term by the previous term: r = \frac{a_{n+1}}{a_n}.

Front

What is the formula for the nth term of an arithmetic sequence?

Back

The formula for the nth term (a_n) of an arithmetic sequence is: a_n = a_1 + (n-1)d.

Front

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

Back

The formula for the nth term (a_n) of a geometric sequence is: a_n = a_1 \cdot r^{(n-1)}.

Front

Identify the first term and common ratio of the sequence: 30, 60, 120, 240...

Back

First term (a_1) = 30; Common ratio (r) = 2.

Front

Determine if the sequence -3, -18, -108, -648 is arithmetic, geometric, or neither.

Back

The sequence is geometric.

Front

What is the common ratio of the sequence 2, 8, 32, 128...?

Back

The common ratio (r) is 4.

Front

Identify if the sequence 4, 9, 14, 19 is arithmetic, geometric, or neither.

Back

The sequence is arithmetic.