WEEK 2C(ALGEBRA 2)

Front

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

Back

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

Front

How do you factor the expression 8x^3 - 1?

Back

The expression 8x^3 - 1 can be factored using the difference of cubes formula: a^3 - b^3 = (a - b)(a^2 + ab + b^2). Thus, it factors to (2x - 1)(4x^2 + 2x + 1).

Front

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

Back

The sum of the first n terms of a geometric series can be calculated using the formula: S_n = a_1 * (1 - r^n) / (1 - r), where a_1 is the first term and r is the common ratio.

Front

What is a geometric series?

Back

A geometric series is the sum of the terms of a geometric sequence, 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 9th term in a geometric sequence?

Back

To find the 9th term in a geometric sequence, use the formula: a_n = a_1 * r^(n-1). For a first term of 3 and a common ratio of 2, the 9th term is 768.

Front

What is the common ratio in a geometric sequence?

Back

The common ratio in a geometric sequence is the factor by which we multiply each term to get the next term. It is calculated as r = a_n / a_(n-1).

Front

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

Back

The first term of the sequence is 4.

Front

What is the common ratio of the sequence 4, -12, 36, -108?

Back

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

Front

How do you determine if a series converges or diverges?

Back

A series converges if the sum of its terms approaches a finite limit as more terms are added. It diverges if the sum grows without bound or does not approach a specific value.

Front

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

Back

The sum of an infinite geometric series can be calculated using the formula: S = a / (1 - r), where a is the first term and |r| < 1.