Subtracting these two equations we then obtain, R S n = a 1 r + a 1 r 2 + a 1 r 3 + … + a 1 r n Multiplying both sides by r we can write, S n = a 1 + a 1 r + a 1 r 2 + … + a 1 r n − 1 Therefore, we next develop a formula that can be used to calculate the sum of the first n terms of any geometric sequence. However, the task of adding a large number of terms is not. For example, the sum of the first 5 terms of the geometric sequence defined by a n = 3 n + 1 follows: is the sum of the terms of a geometric sequence. In fact, any general term that is exponential in n is a geometric sequence.Ī geometric series The sum of the terms of a geometric sequence. In general, given the first term a 1 and the common ratio r of a geometric sequence we can write the following:Ī 2 = r a 1 a 3 = r a 2 = r ( a 1 r ) = a 1 r 2 a 4 = r a 3 = r ( a 1 r 2 ) = a 1 r 3 a 5 = r a 3 = r ( a 1 r 3 ) = a 1 r 4 ⋮įrom this we see that any geometric sequence can be written in terms of its first element, its common ratio, and the index as follows:Ī n = a 1 r n − 1 G e o m e t r i c S e q u e n c e Here a 1 = 9 and the ratio between any two successive terms is 3. For example, the following is a geometric sequence, Get the free view of Chapter 11, Geometric Progression Concise Maths Class 10 ICSE additional questions for Mathematics Concise Maths Class 10 ICSE CISCE,Īnd you can use to keep it handy for your exam preparation.A geometric sequence A sequence of numbers where each successive number is the product of the previous number and some constant r., or geometric progression Used when referring to a geometric sequence., is a sequence of numbers where each successive number is the product of the previous number and some constant r.Ī n = r a n − 1 G e o m e t i c S e q u e n c eĪnd because a n a n − 1 = r, the constant factor r is called the common ratio The constant r that is obtained from dividing any two successive terms of a geometric sequence a n a n − 1 = r. Maximum CISCE Concise Maths Class 10 ICSE students prefer Selina Textbook Solutions to score more in exams. The questions involved in Selina Solutions are essential questions that can be asked in the final exam. Using Selina Concise Maths Class 10 ICSE solutions Geometric Progression exercise by students is an easy way to prepare for the exams, as they involve solutionsĪrranged chapter-wise and also page-wise. Selina textbook solutions can be a core help for self-study and provide excellent self-help guidance for students.Ĭoncepts covered in Concise Maths Class 10 ICSE chapter 11 Geometric Progression are Geometric Progression - Finding Their General Term., Geometric Progression - Finding Sum of Their First ‘N’ Terms, Simple Applications - Geometric Progression. This will clear students' doubts about questions and improve their application skills while preparing for board exams.įurther, we at provide such solutions so students can prepare for written exams. ![]() ![]() ![]() ![]() Selina solutions for Mathematics Concise Maths Class 10 ICSE CISCE 11 (Geometric Progression) include all questions with answers and detailed explanations. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. has the CISCE Mathematics Concise Maths Class 10 ICSE CISCE solutions in a manner that help students Chapter 1: GST (Goods And Service Tax) Chapter 2: Banking (Recurring Deposit Account) Chapter 3: Shares and Dividend Chapter 4: Linear Inequations (In one variable) Chapter 5: Quadratic Equations Chapter 6: Solving (simple) Problems (Based on Quadratic Equations) Chapter 7: Ratio and Proportion (Including Properties and Uses) Chapter 8: Remainder and Factor Theorems Chapter 9: Matrices Chapter 10: Arithmetic Progression Chapter 11: Geometric Progression Chapter 12: Reflection Chapter 13: Section and Mid-Point Formula Chapter 14: Equation of a Line Chapter 15: Similarity (With Applications to Maps and Models) Chapter 16: Loci (Locus and Its Constructions) Chapter 17: Circles Chapter 18: Tangents and Intersecting Chords Chapter 19: Constructions (Circles) Chapter 20: Cylinder, Cone and Sphere Chapter 21: Trigonometrical Identities Chapter 22: Height and Distances Chapter 23: Graphical Representation Chapter 24: Measure of Central Tendency(Mean, Median, Quartiles and Mode) Chapter 25: Probability
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