Recursive and Explicit Formula Practice

Front

What is a recursive formula?

Back

A recursive formula defines the terms of a sequence using previous terms. It specifies how to find the next term based on one or more preceding terms.

Front

What is an explicit formula?

Back

An explicit formula provides a direct way to calculate the nth term of a sequence without needing to know the previous terms.

Front

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

Back

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

Front

What is the explicit formula for a geometric sequence?

Back

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

Front

What is the explicit formula for an arithmetic sequence?

Back

The explicit formula for an arithmetic sequence is a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Front

How do you determine the common difference in an arithmetic sequence?

Back

The common difference is found by subtracting any term from the subsequent term in the sequence.

Front

What is the first term of the sequence 3, 15, 75...?

Back

The first term is 3.

Front

What is the common difference for the sequence -4, -6, -8, -10...?

Back

The common difference is -2.

Front

How do you find the nth term of the sequence 34, 37, 40, 43...?

Back

Use the formula a_n = 34 + (n-1) * 3.

Front

What is the 32nd term of the sequence 34, 37, 40, 43...?

Back

The 32nd term is 127.