Sequences Review

Front

What is a sequence?

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

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

Back

The nth term can be found using the formula: t(n) = a + (n-1)d, where 'a' is the first term and 'd' is the common difference.

Front

What is a common difference?

Back

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

Front

Identify the common difference in the sequence: 3, 7, 11, 15,...

Back

The common difference is 4.

Front

What type of sequence is 2, 4, 8, 16,...?

Back

This is a geometric sequence, where each term is multiplied by a constant factor.

Front

How do you find the 20th term of the sequence: 5, 12, 19, 26...?

Back

First, find the common difference (7), then use the formula: t(20) = 5 + (20-1)7 = 138.

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 the sequence: 2, 6, 18, 54...?

Back

The common ratio is 3.

Front

What does it mean if a sequence is neither arithmetic nor geometric?

Back

It means that the sequence does not have a constant difference or a constant ratio between its terms.