Unit 1 Sequences Test Part 1 (9-11-25)

Front

What is a sequence in mathematics?

Back

A sequence is an ordered list of numbers that follow a specific pattern or rule.

Front

Define an arithmetic sequence.

Back

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

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 explicit formula for an arithmetic sequence?

Back

The explicit formula is given by a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Front

What is the explicit formula for a geometric sequence?

Back

The explicit formula is given by a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Front

How do you find the 100th term of a sequence using the explicit equation?

Back

Substitute n=100 into the explicit formula of the sequence.

Front

What is a recursive definition of a sequence?

Back

A recursive definition defines each term of the sequence based on the previous term(s).

Front

Identify the growth factor in the sequence: 48, 36, 27, 20.25,...

Back

The growth factor is x0.75 (or multiply by 0.75).

Front

How can you determine if a sequence is arithmetic or geometric?

Back

Check if the difference between consecutive terms is constant (arithmetic) or if the ratio of consecutive terms is constant (geometric).

Front

What is the first term of the sequence defined by f(n) = f(n-1) + 4, f(0) = 2?

Back

The first term is f(0) = 2.