(New) Arithmetic or Geometric Sequences

Front

What is an arithmetic sequence?

Back

A sequence of numbers in which the difference between consecutive terms is constant.

Front

What is a geometric sequence?

Back

A sequence of numbers in which 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 common difference in an arithmetic sequence?

Back

The constant amount that is added to each term to get the next term.

Front

What is the common ratio in a geometric sequence?

Back

The constant factor by which we multiply to get from one term to the next.

Front

Identify if the sequence 2, 4, 6, 8, ... is arithmetic, geometric, or neither.

Back

Arithmetic (common difference d = 2).

Front

Identify if the sequence 3, 9, 27, 81, ... is arithmetic, geometric, or neither.

Back

Geometric (common ratio r = 3).

Front

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

Back

a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Front

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

Back

a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Front

Find the 5th term of the arithmetic sequence: 5, 10, 15, ...

Back

25.

Front

Find the 4th term of the geometric sequence: 2, 6, 18, ...

Back

54.