Recursive Sequences

Front

What is a recursive sequence?

Back

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

Front

What is the common difference in an arithmetic sequence?

Back

The constant amount that each term in the sequence increases or decreases by.

Front

How do you find the next term in a recursive sequence?

Back

Use the recursive formula to calculate the next term based on the previous term(s).

Front

What does a₁ represent in a sequence?

Back

The first term of the sequence.

Front

Write the recursive formula for the sequence: 5, 8, 11, 14...

Back

u₁ = 5, u_n = u_n-1 + 3.

Front

What is the explicit formula for an arithmetic sequence?

Back

a_n = a₁ + (n-1)d, where d is the common difference.

Front

Given the sequence: 25, 21, 17, 13..., what is the common difference?

Back

d = -4.

Front

How do you determine the explicit formula for a sequence?

Back

Identify the first term and the common difference, then use the explicit formula for arithmetic sequences.

Front

What is the formula for the nth term of the sequence: 15, 12, 9, 6, 3...?

Back

a_n = 15 - 3(n-1).

Front

What is the significance of the term 'n' in sequences?

Back

It represents the position of a term in the sequence.