Arithmetic and Geometric Sequences

Front

What is the first term of the geometric sequence 30, 60, 120, 240?

Back

The first term, \( a_1 \), is 30.

Front

What is the common ratio of the geometric sequence 30, 60, 120, 240?

Back

The common ratio, \( r \), is 2.

Front

How do you identify an arithmetic sequence?

Back

An arithmetic sequence has a constant difference between consecutive terms.

Front

How do you identify a geometric sequence?

Back

A geometric sequence has a constant ratio between consecutive terms.

Front

What type of sequence is represented by the function \( f(x) = mx + b \)?

Back

This represents an arithmetic sequence.

Front

What type of sequence is represented by the function \( f(x) = a imes r^x \)?

Back

This represents a geometric sequence.

Front

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

Back

The nth term is given by \( a_n = a_1 + (n-1)d \), where \( d \) is the common difference.

Front

What is the formula for the nth term of a geometric sequence?

Back

The nth term is given by \( a_n = a_1 \times r^{(n-1)} \), where \( r \) is the common ratio.

Front

What is the relationship between linear functions and arithmetic sequences?

Back

Linear functions represent arithmetic sequences because they have a constant rate of change.

Front

What is the relationship between exponential functions and geometric sequences?

Back

Exponential functions represent geometric sequences because they involve constant multiplicative growth.