Arithmetic and Geometric Sequences

Front

What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

Front

Define common difference in an arithmetic sequence.

Back

The common difference is the fixed amount added to each term to get the next term in an arithmetic sequence.

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

Define common ratio in a geometric sequence.

Back

The common ratio is the factor by which we multiply each term to get the next term in a geometric sequence.

Front

Identify the common difference in the sequence: 10, 15, 20, 25,...

Back

5

Front

Identify the common ratio in the sequence: 3, 9, 27, 81,...

Back

3

Front

Is the sequence 2, 4, 8, 16,... geometric?

Back

Yes

Front

What is the 5th term of the sequence a(n) = 3n + 2?

Back

17

Front

Is the sequence 5, 10, 15, 20,... arithmetic, geometric, or neither?

Back

Arithmetic

Front

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

Back

The nth term is given by a(n) = a + (n-1)d, where a is the first term and d is the common difference.