Using Recursive/Explicit

Front

What is a recursive sequence?

Back

A recursive sequence is a sequence in which each term is defined as a function of one or more of its preceding terms.

Front

What is an explicit formula?

Back

An explicit formula defines the nth term of a sequence directly in terms of n, without referencing previous terms.

Front

How do you find the common ratio in a geometric sequence?

Back

The common ratio (r) is found by dividing any term by the previous term in the sequence.

Front

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

Back

The nth term 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

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

Back

r = -1/4.

Front

What are the next three terms in the sequence 4, 12, 36, 108?

Back

The next three terms are 324, 972, 2916.

Front

If a_1 = -3 and a_n = a_{n-1} * 3, what are the first three terms?

Back

The first three terms are -3, -9, -27.

Front

What recursive formula describes the sequence 2, -6, 18, -54?

Back

a_n = a_{n-1} * -3, a_1 = 2.

Front

What is the recursive formula for geometric sequences?

Back

The recursive formula is a_n = a_{n-1} * r.

Front

What is the first term of the sequence defined by a_n = 2^n?

Back

The first term (a_1) is 2.