Optional Mid Cycle 3 Review (11/21)

Front

What is the explicit formula for a geometric sequence?

Back

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

Front

What is the result of dividing \( \frac{9x^2}{-3x} \)?

Back

The result is -3x.

Front

What is the product of (6r)(5r^2)?

Back

The product is 30r^3.

Front

How do you identify the common difference in an arithmetic sequence?

Back

The common difference is found by subtracting any term from the subsequent term. For example, in the sequence 10, 20, 30, 40, the common difference is 20 - 10 = 10.

Front

What is the equivalent expression for \( (a^2 + 9a - 1)(-4a + 3) \)?

Back

The equivalent expression is -4a^3 - 33a^2 + 31a - 3.

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 formula for the nth term of an arithmetic sequence?

Back

The nth term of an arithmetic sequence can be calculated 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 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

What is the result of \( 6r \times 5r^2 \)?

Back

The result is 30r^3.

Front

How do you simplify the expression \( \frac{9x^2}{-3x} \)?

Back

To simplify, divide the coefficients and subtract the exponents of x: \( \frac{9}{-3} = -3 \) and \( x^{2-1} = x \), resulting in -3x.