Review

Front

Find the distance between the points (1, 2) and (4, 6).

Back

The distance between two points (x1, y1) and (x2, y2) is given by the formula: \(d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}\). For points (1, 2) and (4, 6), the distance is \(d = \sqrt{(4 - 1)^2 + (6 - 2)^2} = \sqrt{9 + 16} = \sqrt{25} = 5\).

Front

Find the midpoint of the line segment joining the points (3, 4) and (7, 8).

Back

The midpoint M of a line segment joining points (x1, y1) and (x2, y2) is given by: \(M = \left(\frac{x1 + x2}{2}, \frac{y1 + y2}{2}\right)\). For points (3, 4) and (7, 8), the midpoint is \(M = \left(\frac{3 + 7}{2}, \frac{4 + 8}{2}\right) = (5, 6)\).

Front

What is the common difference in the arithmetic sequence: 3, 7, 11, 15, ...?

Back

In an arithmetic sequence, the common difference d is found by subtracting any term from the subsequent term. Here, d = 7 - 3 = 4.

Front

In the geometric sequence 5, 15, 45, 135, ..., what is the common ratio?

Back

In a geometric sequence, the common ratio r is found by dividing any term by the previous term. Here, r = 15 / 5 = 3.

Front

Back

To solve for x, subtract 3 from both sides: \(2x = 8\). Then divide by 2: \(x = 4\).

Front

What is the formula for the distance between two points in a coordinate plane?

Back

The formula for the distance d between two points (x1, y1) and (x2, y2) is: \(d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}\).

Front

How do you find the midpoint of a line segment?

Back

To find the midpoint M of a line segment joining points (x1, y1) and (x2, y2), use the formula: \(M = \left(\frac{x1 + x2}{2}, \frac{y1 + y2}{2}\right)\).

Front

Define an arithmetic sequence.

Back

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

Front

Define 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 common difference in an arithmetic sequence?

Back

The common difference d in an arithmetic sequence is the constant amount that each term increases or decreases by, calculated as d = term(n+1) - term(n).