The table shows the heights of a bungee jumpers bounces. Sequences and series make this foldable to help you organize your notes. The number r is called the common ratio because any two consecutive terms of the sequence. The general term of a geometric sequence where n is a positive. Cbse class 11 mathematics revision notes chapter9 sequences and series class 11 notes mathematics. Notes hw blank wednesday, march 1 modeling with sequences notes thursday, march 2 late start task schlimgen hw key notes key friday, march 3 no school. Find the common ratio of the following sequence 8, 20, 50, 125, 6. Find the common difference in each of the following arithmetic sequences. A geometric sequence is a sequence in which the ratio of any term to the previous term is constant. Geometric means the terms between any two nonconsecutive terms of a geometric sequence are called geometric means. The definitions imply convenient formulas for the nth term of both. It includes some worked examples, some mwbs for them to try and then some questions to do in their books with answers. Geometric sequences higher gcse questions teaching resources.
The height of the bounces shown in the table above form a geometric sequence. Write a simplified form of the geometric sequence with a4 18 and a12 118098. These notes are sefcontained, but two good extra references for this chapter are tao, analysis i. Clonedcopied questions from previous 91 edexcel gcse exams. Summary notes and examples grade 11 revision before you begin working with grade 12 patterns, sequences and series, it is important to revise what you learnt in grade 11 about quadratic sequences. Arithmetic and geometric sequences a sequence in which the difference between any term and the term before is a constant is an arithmetic sequence.
Arithmetic and geometric sequences notes worksheets. The common ratio can be found by dividing any term by its previous term. In a geometric sequence, the ratio of successive terms is the same number r, called the common ratio. Are the following sequences, arithmetic, geometric, or neither. S n n i ari 1 1 1 sums of a finite geometric series o the sum of the first n terms of a geometric series is given by. The distinguishing feature of a geometric sequence is that the ratio formed by dividing any term the nth term by the preceding term the n1 th term is a constant. For the following problems, write the recursive formula and find the next two terms.
The class will continue to explore sequences as we complete the following two partner activities. Write a sequence that has two geometric means between 48 and 750. To establish basic elements of arithmetic sequences and series example 1. Why you should learn it goal 2 goal 1 what you should learn 11. Use geometric sequences and series to model reallife quantities, such as monthly bills for cellular telephone service in example 6. Find the common ratio in each of the following geometric sequences. Write a simplified form of the geometric sequence with a1 128 and a8 2187. It also explores particular types of sequence known as arithmetic progressions aps and geometric progressions gps, and the corresponding series. Consider the arithmetic sequence 3, 7, 11, 15, 19, what does the mean.
Any term of a geometric sequence of common ratio is obtained from the term by the relation a r a. I can write an explicit rule for a geometric sequence. Write a simplified form of the geometric sequence with a6 8 and a 1024. Main ideasquestions notes geometric sequences a sequence in which the pattern of the sequence is being multiplied common ratio fraction 2 1,3 2,4. The next term in this sequence is of course 48, since each term is twice the last one. Then, if m belongs to all real numbers outside the range 0,1, if m lies in between 0 and 1, if m is equal to 0 or 1. Geometric series notes geometric series the s of the terms of a geometric sequence. Define a finite geometric series and find the common ratio. Sep 25, 2016 attached is a ppt i made for my top set year 11 to teach them geometric progressions sequences as part of the new gcse. Reading and writingas you read and study the chapter, fill the journal with examples for each lesson. A quadratic sequence is a sequence in which the second difference is constant. Decide when realworld problems model a geometric sequence and write the equation to model the situation 9. Notes geometric sequence and series common ratio, r h.
Write an equation for a geometric sequence use an equation to find the nth term of a geometric sequence notes. Geometic sequences geometric sequences multiplied common. Grieser page 3 geometric series a geometric series is the sum of the terms in a geometric sequence. Derive the formula for the sum of a finite geometric series, s n a 1 1 r n. Its important to understand what is meant by convergence of series be fore getting to numerical analysis proper. Begin with one sheet of 11 by 17 paper and four sheets of notebook paper. Given a term in a geometric sequence and the common ratio find the first five terms, the explicit formula, and the recursive formula.
The sequence an is a geometric sequence with first term a and common ratio r. Geometric sequences a geometric sequence is a sequence where each term is found by multiplying the previous term by a constant called the common ratio r. To solve reallife problems, such as finding the number of tennis matches played in exs. For these activities, i think it is best to group my students into. It also explores particular types of sequence known. Clark college winter 2008 john mitchell page 4 of 8 geometric sequences in a geometric sequence the ratio between successive terms is constant, to get the next term i multiply the current term by a constant. Finite geometric series a series with a n number of terms. Geometric sequence and series an hdi atl rn, where r 1 4 l. For a geometric sequence a n a 1 r n1, the sum of the first n terms is s n a 1. Analyze arithmetic sequences and series to solve problems.
Deriving the formula to calculate the n th term, given a geometric sequence. Module 2 arithmetic and geometric sequences classroom task. Geometric sequences higher gcse questions teaching. The explicit formula for a geometric sequence is of the form a n a 1 r1, where r is the common ratio.
An explicit formula for this geometric sequence is given by an arn. Arithmetic and geometricprogressions mctyapgp20091 this unit introduces sequences and series, and gives some simple examples of each. A develop understanding task representing arithmetic sequences with. Construct geometric sequences given a graph, description or table. Geometric sequence and series an hdi atl rn, where r 1 4 l ri 01. Attached is a ppt i made for my top set year 11 to teach them geometric progressionssequences as part of the new gcse. It is found by taking any term in the sequence and dividing it by its preceding term. Geometric sequences notes in a flap book is perfect for your interactive notebook. In our study of geometric sequences, we learned that the formula for the th term of a geometric8 sequence has the form, where is the common ratio. Chapter 6 sequences and series in this unit, we will identify an arithmetic or geometric sequence and find the formula for its nth term determine the common difference in an arithmetic sequence determine the common ratio in a geometric sequence.
Geometric sequences the height of the first rebound of the ball is 30. Geometric sequences in a geometric sequence the ratio between successive terms is constant, to get the next term i multiply the current term by a constant. Grieser page 2 finding terms in a geometric sequence o find the 7th term in the sequence. Let x 1, x 2, x n be n positive real numbers and let m be a real number. A geometric series x1 n0 a n is a series in which each term is a xed multiple of the previous one. For a geometric sequence, a formula for thenth term of the sequence is a n 5 a rn21.
V f2 50s1 2q 7k 6u rtra1 jsovfpt9w ra aree b alal 9c m. I can identify a geometric sequence and state its common ratio. Unit g geometric sequences class notes completed no need to copy notes from overhead basic elements of arithmetic sequences and series objective. Sequences and series class 11 notes mathematics mycbseguide. See attached geometric sequences notes for a description of how this is done.
Sequences geometric sequences main ideasquestions notes. Chapter 11 sequences and series 577 sequences and seriesmake this foldable to help you organize your notes. Notes,whiteboard,whiteboard page,notebook software,notebook, pdf,smart,smart technologies ulc,smart board interactive whiteboard created date. The formula for a geometric sequence is always an exponential function. Write each of the sequences from examples 5, 6, and 7 using a recursive rule. Sequence and series notes for iit jee, download pdf. Weighted geometric meang weighted harmonic meanh equality holds when all the entries are equal. In an arithmetic sequence thedifference between successive terms,a n11 2 a n,is always the same, the constant d. This unit introduces sequences and series, and gives some simple examples of each. Eighth grade lesson geometric and arithmetic sequences.
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