Recursive Sequences

Front

What is a recursive sequence?

Back

A recursive sequence is a sequence of numbers where each term is defined as a function of one or more of the preceding terms.

Front

What is the recursive rule for the Fibonacci sequence?

Back

f_n = f_{n-1} + f_{n-2}, with f_1 = 1 and f_2 = 1.

Front

Given a recursive formula a_n = a_{n-1} + d, what does 'd' represent?

Back

'd' represents the common difference between consecutive terms in an arithmetic sequence.

Front

How do you find the first four terms of a recursive sequence?

Back

Start with the initial term(s) and apply the recursive rule repeatedly to find subsequent terms.

Front

What is the first term of the sequence defined by a_n = 3a_{n-1} - 1 if a_1 = 5?

Back

The first term a_1 is 5.

Front

Write the recursive rule for the sequence 2, 4, 8, 16, ...

Back

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

Front

What is the difference between a recursive sequence and an explicit formula?

Back

A recursive sequence defines each term based on previous terms, while an explicit formula allows you to calculate any term directly.

Front

If a_1 = 10 and a_n = a_{n-1} - 2, what is a_4?

Back

a_4 = 10 - 2*3 = 4.

Front

What is the recursive formula for the sequence defined by a_n = 5n - 3?

Back

a_1 = 2, a_n = a_{n-1} + 5.

Front

How do you determine the nth term of a recursive sequence?

Back

You apply the recursive rule starting from the initial term until you reach the nth term.