Problem 72 - Algebra and Trigonometry

Question

What is an arithmetic sequence? Give an example with your explanation.

Step-by-Step Solution

Answer

An arithmetic sequence is a sequence of numbers in which each term after the first is obtained by adding a constant difference to the preceding term. For example, in the sequence 2, 4, 6, 8, 10,... the constant difference is 2.

Step 1: Definition of an Arithmetic Sequence

An arithmetic sequence is a sequence of numbers in which any term after the first is obtained by adding a constant difference to the preceding term. This constant difference is often written as 'd'.

Step 2: Explain constant difference

\(d\) can be found by subtracting the first term from the second term in the sequence. For instance, if the sequence is denoted as \( a_1, a_2, a_3, ..., a_n \), then \(d = a_2 - a_1\). This difference remains the same throughout the sequence.

Step 3: Provide an example

A common example of an arithmetic sequence is 2, 4, 6, 8, 10,... Here, the constant difference \(d\) is 2, as each term is 2 greater than the previous term.