*Try it risk-free After completing this lesson, you will be able to recognize an arithmetic sequence.*

*Try it risk-free After completing this lesson, you will be able to recognize an arithmetic sequence.*

In 1943, in response to the French National Organisation for Standardisation's (AFNOR) requirement for standardising all the objects involved in the construction process, Le Corbusier asked an apprentice to consider a scale based upon a man with his arm raised to 2.20 m in height.

The result, in August 1943 was the first graphical representation of the derivation of the scale.

On 10 January 1946 during a visit to New York, Le Corbusier met with Henry J.

Kaiser, an American industrialist whose Kaiser Shipyard had built Liberty ships during World War II.

Let's look at a couple of examples of an arithmetic sequence: 7, 11, 15, 19, …

6, 9, 12, 15, 18 The first example starts at the number seven, and the constant difference between consecutive terms is four.An arithmetic sequence is a list of numbers in which the difference between consecutive terms is constant.An arithmetic sequence can start at any number, but the difference between consecutive terms must always be the same.As a member, you'll also get unlimited access to over 79,000 lessons in math, English, science, history, and more.Plus, get practice tests, quizzes, and personalized coaching to help you succeed.The common difference in the following sequence is -2.5. Now, let's look at a non-example: 3, 8, 15, 24, 35, … The nth term of a sequence will be represented by a(n). We can see that the common difference between consecutive terms is 5. We can extend the list as follows until we get to the 7th term: -3, 2, 7, 12, 17, 22, 27, … Let's take the same sequence from the previous example, except we now have to find the 33rd term or a(33).This is not an arithmetic sequence because the difference between consecutive terms is not the same. For instance, the 1st term of a sequence is a(1) and the 23rd term of a sequence is a(23). We could use the same method as before, but it will require lengthy work. To get from a(1) to a(33), we would need to add 32 consecutive terms (33 - 1 = 32).With the Modulor, Le Corbusier sought to introduce a scale of visual measures that would unite two virtually incompatible systems: the Anglo Saxon foot and inch and the French metric system.Whilst he was intrigued by ancient civilisations who used measuring systems linked to the human body: elbow (cubit), finger (digit), thumb (inch) etc., he was troubled by the metre as a measure that was a forty-millionth part of the meridian of the earth.The numbers next to the a are usually written as subscripts, but parentheses will be used at times in this lesson. We need to come up with a quicker and more efficient method. Therefore, we are adding 5 thirty-two times to the first term. The problem is completed below: a(33) = -3 (33 - 1)5 = -3 32*(5) = -3 160 = 157.The general formula or rule for an arithmetic sequence is shown in Figure 2.

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