Margie's Recursive Sequence Flashcard 2024

Front

What is a recursive sequence?

Back

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

Front

Write the recursive formula for the sequence 6, 17, 28, 39, 50.

Back

The recursive formula is: a_n = a_{n-1} + 11, with a_1 = 6.

Front

What is the difference between an arithmetic sequence and a geometric sequence?

Back

An arithmetic sequence has a constant difference between consecutive terms, while a geometric sequence has a constant ratio between consecutive terms.

Front

Determine if the sequence 200, 100, 50, 25, ... is arithmetic or geometric.

Back

The sequence is geometric.

Front

Write the recursive formula for the sequence 7, 14, 28, 56, 112, ...

Back

The recursive formula is: a_n = a_{n-1} \cdot 2, with a_1 = 7.

Front

Identify an arithmetic sequence from the following: 1, 3, 5, 7, 9, ...; 1, 2, 4, 8, 16, 32, ...; 1, 1, 2, 3, 5, 8, 13, ...

Back

The arithmetic sequence is 1, 3, 5, 7, 9, ...

Front

What is the formula to find the nth term of an arithmetic sequence?

Back

The nth term can be found using the formula: a_n = a_1 + (n-1)d, where d is the common difference.

Front

What is the formula to find the nth term of a geometric sequence?

Back

The nth term can be found using the formula: a_n = a_1 \cdot r^{(n-1)}, where r is the common ratio.

Front

Find the eighth term of the sequence 3, 6, 12, 24, ...

Back

The eighth term is 384.

Front

What is a common difference in an arithmetic sequence?

Back

The common difference is the fixed amount added to each term to get the next term in an arithmetic sequence.