Geometric Sequence and Exponential Function review

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

What is 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 common difference in an arithmetic sequence.

Back

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

Front

How do you find the common difference in the sequence 25, 13, 1, -11?

Back

Subtract the first term from the second term: 13 - 25 = -12. The common difference is -12.

Front

What characterizes a linear function?

Back

A linear function is characterized by a constant rate of change, represented graphically as a straight line.

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent.

Front

How can you identify if a table of values represents a linear or exponential relationship?

Back

If the differences between consecutive y-values are constant, it is linear. If the ratios of consecutive y-values are constant, it is exponential.

Front

Find the next term in the geometric sequence 81, 9, 1, 1/9.

Back

The next term is 1/81, found by multiplying the last term (1/9) by the common ratio (1/9).

Front

What is the common ratio in the sequence 81, 9, 1, 1/9?

Back

The common ratio is 1/9, calculated by dividing any term by the previous term (e.g., 9/81 = 1/9).

Front

What does it mean for a function to be exponential?

Back

A function is exponential if it grows or decays at a rate proportional to its current value, leading to rapid increases or decreases.