Practice Arithmetic Explicit & Recursive Sequences

Front

What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is called the common difference.

Front

How do you find the explicit formula for an arithmetic sequence?

Back

The explicit formula for the n-th term of an arithmetic sequence can be expressed as: a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Front

What is the common difference in an arithmetic sequence?

Back

The common difference (d) is the constant amount that each term increases or decreases by in an arithmetic sequence.

Front

Given the sequence 2, 9, 16, 23, what is the common difference?

Back

The common difference is 7.

Front

What is the first term (a_1) in the sequence -6, -14, -22, -30?

Back

The first term a_1 is -6.

Front

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

Back

To find the first four terms of a recursive sequence, start with the initial term and apply the recursive formula repeatedly.

Front

What is the recursive formula for the sequence where a_1 = -16 and a_n = a_{n-1} + 5?

Back

The recursive formula is a_n = a_{n-1} + 5, starting with a_1 = -16.

Front

What is the explicit formula for the sequence 2, 9, 16, 23?

Back

The explicit formula is a_n = 2 + 7(n-1).

Front

How do you find the 26th term in the sequence -15, -35, -55, -75?

Back

Use the explicit formula: a_n = -15 - 20(n-1). For n=26, a_{26} = -15 - 20(25) = -515.

Front

What is the formula to find the n-th term of an arithmetic sequence?

Back

The formula is a_n = a_1 + (n-1)d.