Geometric Sequences

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 (r) in a geometric sequence?

Back

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

Front

Is the sequence -432, 72, -12, 2,... geometric?

Back

Yes, this sequence is geometric because each term is obtained by multiplying the previous term by a common ratio.

Front

What is 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

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

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

Back

The 4th term is a_4 = 3 * 4^(4-1) = 3 * 64 = 192.

Front

Daisy received $2 on her first birthday. Each year, the amount of money she received tripled. How much money will she receive on her 5th birthday?

Back

Daisy will receive $162 on her 5th birthday.

Front

What is the formula to find the nth term of a geometric sequence?

Back

The formula to find the nth term of a geometric sequence is a_n = a_1 * r^(n-1).

Front

If a geometric sequence has a common ratio of 2, what are the first three terms if the first term is 5?

Back

The first three terms are 5, 10, and 20.

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.