BR 11/6/24 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 determine if a sequence is geometric?

Back

A sequence is geometric if the ratio of any two consecutive terms is constant.

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 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 2, what is the 4th term?

Back

The 4th term can be calculated as: a_4 = 3 * 2^(4-1) = 3 * 8 = 24.

Front

What is the common ratio of the sequence 5, 15, 45, 135?

Back

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

Front

Can a geometric sequence have a common ratio of 0?

Back

No, a geometric sequence cannot have a common ratio of 0, as this would make all subsequent terms equal to 0.

Front

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

Back

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

Front

If a geometric sequence has a common ratio of -4, what happens to the signs of the terms?

Back

The signs of the terms will alternate; if the first term is positive, the second will be negative, the third will be positive, and so on.

Front

How can you find the common ratio from the first two terms of a geometric sequence?

Back

The common ratio can be found by dividing the second term by the first term: r = a_2 / a_1.