Algebra 2B Module 07

Front

What is an infinite geometric series?

Back

An infinite geometric series is the sum of the terms of an infinite geometric sequence, where each term is found by multiplying the previous term by a constant called the common ratio.

Front

What condition must be met for an infinite geometric series to converge?

Back

The absolute value of the common ratio (r) must be less than 1 (|r| < 1). If |r| ≥ 1, the series diverges.

Front

Identify the common ratio in the series: 2, 6, 18, 54.

Back

The common ratio is 3, as each term is multiplied by 3 to get the next term.

Front

What is the formula for the sum of an infinite geometric series?

Back

S = a / (1 - r), where 'a' is the first term and 'r' is the common ratio.

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

How do you find 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 difference between a geometric sequence and an arithmetic sequence?

Back

In a geometric sequence, each term is multiplied by a constant (common ratio), while in an arithmetic sequence, each term is added to a constant (common difference).

Front

If a job pays $50,000 in the first year and increases by $1,000 each year, what will the salary be in 10 years?

Back

$59,000.

Front

What is the common difference in the sequence defined recursively as a1 = 3, an = an-1 + 5?

Back

The common difference is 5.

Front

What is the first term of the geometric sequence 4, 12, 36, 108?

Back

The first term is 4.