Recursive and Arithmetic 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 first term of the sequence defined by a_n = a_{n-1} + 5 with a_1 = -16?

Back

The first term is -16.

Front

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

Back

Start with the first term and use the recursive formula to calculate subsequent terms.

Front

What is the common difference in an arithmetic sequence?

Back

The common difference is the constant amount that each term increases or decreases by.

Front

Write the recursive formula for the sequence 10, 5, 0, -5,...

Back

a_1 = 10, a_n = a_{n-1} - 5.

Front

What is the explicit formula for an arithmetic sequence?

Back

The explicit formula is a_n = a_1 + (n-1)d, where d is the common difference.

Front

Given the sequence 15, 12, 9, 6, 3, what is the recursive formula?

Back

a_1 = 15, a_n = a_{n-1} - 3.

Front

How do you determine the next term in a sequence?

Back

Use the recursive formula or the explicit formula to calculate the next term.

Front

What does the slope represent in the context of a linear equation related to sequences?

Back

The slope represents the common difference in an arithmetic sequence.

Front

If a_n = 7 in the sequence 2, 7, 12, 17,..., what is a_{n+1}?

Back

a_{n+1} = 12.