Hon IM1 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 in a geometric sequence?

Back

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

Front

Given the sequence 64, -16, 4, -1, what is the common ratio?

Back

r = -1/4.

Front

What is a recursive formula for a geometric sequence?

Back

A recursive formula defines each term based on the previous term, typically in the form a_n = r * a_(n-1), where r is the common ratio.

Front

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

Back

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

Front

Identify the recursive formula for the sequence 2, -6, 18, -54.

Back

a_n = a_(n-1)(-3), a_1 = 2.

Front

What is the explicit formula for the nth term of a geometric sequence with a_4 = 108 and r = -2?

Back

a_n = -13.5 * (-2)^(n-1).

Front

How do you convert a recursive formula to an explicit formula?

Back

To convert, identify the first term and the common ratio, then use the formula a_n = a_1 * r^(n-1).

Front

What is the first term of the sequence defined by a_n = -4n - 1?

Back

The first term (a_1) is -5.

Front

What are the first four terms of the sequence defined by a_n = -4n - 1?

Back

The first four terms are -5, -9, -13, -17.