Algebra 2 Unit 1 Lesson 1-7 review

Front

What is a recursive definition of a sequence?

Back

A recursive definition specifies the first term of a sequence and a rule for determining subsequent terms based on previous terms.

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

How do you find the first five terms of a recursive sequence?

Back

Start with the first term and apply the recursive rule repeatedly to find subsequent terms.

Front

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

Back

The nth term can be found using the formula: a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Front

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

Back

The nth term can be found using the formula: a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Front

What is the sum of the first n terms of an arithmetic sequence?

Back

The sum can be calculated using the formula: S_n = n/2 * (a_1 + a_n), where a_n is the nth term.

Front

What is the sum of the first n terms of a geometric sequence?

Back

The sum can be calculated using the formula: S_n = a_1 * (1 - r^n) / (1 - r), for r ≠ 1.