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 common ratio in a geometric sequence?

Back

The common ratio (r) can be found by dividing any term by the previous term in the sequence (r = a_n / a_(n-1)).

Front

What does 'r' represent in a geometric sequence?

Back

In a geometric sequence, 'r' represents the common ratio, which is the factor by which we multiply each term to get the next term.

Front

Write the explicit formula for a geometric sequence.

Back

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

Front

If the first term of a geometric sequence is 4 and the common ratio is 3, what is the 5th term?

Back

The 5th term is a_5 = 4 * 3^(5-1) = 4 * 81 = 324.

Front

What is the formula to find 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).

Front

If a geometric sequence has a common ratio of -2, what is the second term if the first term is 5?

Back

The second term is a_2 = 5 * (-2) = -10.

Front

Calculate the 12th term of the sequence: -1, -3, -9, -27, ...

Back

The 12th term a_12 = -1 * (-3)^(12-1) = -1 * (-3)^(11) = -177,147.

Front

In the sequence where Daisy received $2 on her first birthday and the amount tripled each year, how much will she receive on her 5th birthday?

Back

Daisy will receive $162 on her 5th birthday.

Front

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

Back

The sum of the first n terms (S_n) of a geometric sequence is given by S_n = a_1 * (1 - r^n) / (1 - r) for r ≠ 1.