9. Arithmetic vs 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

What is the common difference in an arithmetic sequence?

Back

The common difference is the fixed amount added to each term to get the next term in the 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

What is the 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 the sequence.

Front

In the sequence 9, 18, 27, 36, what is the common difference?

Back

9

Front

In the sequence -2, -4, -8, -16, what is the common ratio?

Back

2

Front

How can you identify an arithmetic sequence from a graph?

Back

An arithmetic sequence will show a straight line when graphed, indicating a constant rate of change.

Front

How can you identify a geometric sequence from a graph?

Back

A geometric sequence will show an exponential curve when graphed, indicating a multiplicative rate of change.

Front

If the first term of an arithmetic sequence is 4 and the common difference is 4, what is the 7th term?

Back

28

Front

If the first term of a geometric sequence is 3 and the common ratio is 2, what is the 4th term?

Back

24