Knowing that the sequence is arithmetic allows us to use the pattern of an arithmetic sequence in order to find the general term. If we did not know something of the pattern then our task of finding the general term would be much more difficult. On the flip side, when we need to PROVE that a sequence is arithmetic we must show that the sequence follows the pattern of an arithmtic sequence.
Explore and Extend 40 minutes This lesson parallels that of the previous day. Here, we focus our attention on geometric patterns and learn the formal methods of defining geometric number patterns explicitly and recursively. In this lesson, we focus on the geometric sequences from this activity.
Using the sequence strips labeled bgh and jI ask students to work together to come up with a rule that expresses the term in terms of n, the term's position in the sequence [MP7].
As students work together, I offer support and hints as necessary. When students have had time to develop these rules, I ask them to share their ideas using a quick poll on the TI NSpire Navigator System.
When we have a collection to look at, we check each idea together to see if substituting 1 for n yields the correct initial term, 2 for n yields the correct second term, etc. This leads to a discussion of sequence notation and how it is similar to and different from exponential function notation.
After the group discussion of student findings, I write the formulas on the board and we work a few examples of using the formulas to find the nth term, the term number, or the common ratio. We also examine the graph of a geometric sequence and compare it to the graph of an exponential function.
Students take note of the formulas, illustrations and examples that I write on the board and actively participants in the discussion. During this time I circulate with a clipboard to note problems that students are having both with the math content and with remaining on task.
I stop to ask questions and give hints as necessary. After students have worked for 10 or 15 minutes, I share answers to the exercises and answer any questions that came up for students.Given a geometric sequence with the first term a1 and the common ratio r, the nth (or general) term is given by Menu.
About Academic Tutoring Finding the n th Term of a Geometric Sequence Given a Substitute this expression for a 1 in the second equation and solve for r.
3. Arithmetic Sequences and Sums Sequence. A Sequence is a set of things (usually numbers) that are in order.. Each number in the sequence is called a term (or sometimes "element" or "member"), read Sequences and Series for more details..
Arithmetic Sequence. In an Arithmetic Sequence the difference between one term and the next is a constant..
In other words, we just add the same value each time. May 03, · For 5a, first think about the sequence [tex]7, 8, 9, \cdots[/tex]. How would you express the general term for that? Once you've thought about it, can you see a way to use the same trick I pointed out for 5b to get the sequence the question asks for?
Given that the 2nd and 5th term of a geometric sequence is 20 and , the formula will be obtained as follows. The formula for geometric sequence is given by: nth=ar^(n-1). For example, if you are asked to find an expression for the nth term of the sequence that starts 5, 8, 11, 14, then find the common difference, which in this case is 3 so 3n is in the formula.
So for n = 1 3n is 3 so add 2 to get to the term 5. The 3rd term of the Series (65) is the sum of the first three terms of the underlying sequence (5 + 15 + 45), and is typically described using Sigma Notation with the formula for the Nth term of an Geometric Sequence (as derived above).