Arithmetic & 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. For example, 2, 5, 8, 11 is an arithmetic sequence with a common difference of 3.

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. For example, 3, 6, 12, 24 is a geometric sequence with a common ratio of 2.

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What is the slope of the line that passes through (2,4) and (6,12)?

Back

The slope is 2.

Front

What is the slope of the line that passes through (5,-10) and (5,-4)?

Back

The slope is undefined because the x-coordinates are the same, indicating a vertical line.

Front

What is the slope of the line that passes through (-4,7) and (-6,-4)?

Back

Front

Is the sequence 7, 7, 7, 7, ... arithmetic, geometric, or neither?

Back

The sequence is geometric because each term is the same, which can be considered as multiplying by a common ratio of 1.

Front

Is the sequence 2, 8, 32, 128, ... arithmetic, geometric, or neither?

Back

The sequence is geometric with a common ratio of 4.

Front

What is the common difference in an arithmetic sequence?

Back

The common difference is the constant amount that each term increases or decreases by in an arithmetic sequence.

Front

What is the common ratio in a geometric sequence?

Back

The common ratio is the fixed number that each term is multiplied by to get the next term in a geometric sequence.