Topics Topic 1—Algebra 1.1 The nth term of an arithmetic sequence The sum of n terms of an arithmetic sequence The nth term of a geometric sequence un = u1 + (n − 1)d S n= n n (2u1 + (n − 1)d ) = (u1 + un ) 2 2 un = u1r n −1 The sum of n terms of a u1 (r n − 1) u (1 − r n ) ‚ r ≠1 = = 1 Sn finite geometric sequence r −1 1− r The sum of an infinite geometric sequence 1.2 Exponents and logarithms Laws of logarithms S∞ = u1 ‚ r 0 − cos ∫ sin x dx = x + C = ∫ cos x dx sin x + C ∫e
Premium Volume Geometry Rectangle
In this week’s assignment I will attempt complete exercises 35 and 37 in the “Real World Applications” section on page 280 of Mathematics in Our World. For each exercise‚ specify whether it involves an arithmetic sequence or a geometric sequence and use the proper formulas where applicable. I will try to format my math work as shown in the “week one assignment guide” provided to us and try to be concise in my reasoning. Exercise 35: A person hired to build a CB Radio tower. The firm charges
Premium Geometric progression Sequence
73 5 121 6 181 Students are expected to make the stellar shape for the next to stages and count the no of dots to get the 6-stellar number in 5th and 6th stage Diagrams can be hand made or using technology Communication or observation of the number pattern has to be given From the observation‚ the expression of the terms of this sequence has to be identified Expression for the 7th term General expression 6 – stellar shape
Premium Sequence Natural number Mathematics
the third term of a geometric progression is 20 and the sum of its first three terms is 26. Find the progression. (a) 2‚ 6‚ 18… (b) 18‚ 6‚ 2‚… (c) Both of these (d) Cannot be determined 4. The sum of 5 numbers in AP is 30 and the sum of their squares is 220. Which of the following is the third term? (a) 5 (b) 6 (c) 8 (d) 9 5. Find the general term of the GP with the third term 1 and the seventh term 8. (a) (23/4)n-3 (b) (23/2)n-3 (c) (23/4)3-n (d) None of these Four geometric means are inserted
Premium Arithmetic mean Sequence Series
Core 1 Linear Graphs and Equations For any straight line‚ the gradient (M) is: dy/dx or difference in y/difference in x which is (y2-y1)/(x2-x1) Equation of a line: y=mx+c which is used when the gradient and intercept is known or y-y1=m(x-x1) when the gradient and the co-ordinates (x1‚y1) of a single point that the line passes through is known. You’ll need to learn this equation. [The equation of the line can be kept in this form unless stated in the exam. (reduces error chance) Also
Premium Angle Real number Geometric progression
cost for the first month when the baby was born was RM22. What a) were the expenses for the 10th month and the 15th month after the baby was born? (4m) b) were the total expenses for the first two years? (3m) 3. Three successive terms of a geometric sequence are x – 6 ‚ x and 9 + 2x. All the terms of the sequence are positive. a) Find x. (2m) b) If x is the fifth term‚ find the first term of the sequence. (2m) 4. The monthly maintenance cost of a car increases by 2% from the previous month’s
Premium Geometric progression Mathematics Sequence
Thomas Malthus Principles of Population Today‚ there is both agreement and disagreement of Thomas Malthus’ essay on the principles of population. Malthus stated that population grows exponentially or at “geometric rate” and food production grows at arithmetic rate‚ or linearly. Geometric rate grows in a series of numbers (2‚4‚8‚16‚32…etc.)‚ which shows that children will grow up and each have their own children‚ and those children will have their own children. Eventually the base numbers of children
Premium United States Demography Population
Additional Mathematics Project Work 2 Written By : Nurul Hazira Syaza Abas I/C : 940602-01-6676 Angka Giliran : School : SMK Kangkar Pulai Copyright 2011 ©. Hazira Syaza‚ All Right Reserve Numb | Title | Page | 1 | Acknowledge | 1 | 2 | Objective | 2 | 3 | Introduction Part I | 3 | 4 | Mathematics In Cake Baking And Cake Decorating | 4 5 | 5 | Part II | 6 14 | 6 | Part III | 15 17 | 7 | Further Exploration | 18 21 | 8 | Reflection | 22 23 | 9 | Conclusion | 24
Premium Length Geometric progression Baking
Susan Dellinger: Psycho-Geometrics I love great public speakers. I’ve seen some great ones in my life. They captivate the audience‚ entertain‚ educate‚ even make you laugh. The most important part is that they make it look effortless and natural. Susan Dellinger‚ the speaker for the video‚ "Psycho-Geometrics" is one of them. Her presentation was incredibly entertaining‚ interesting‚ and funny. But the focal point was definitely Ms. Dellinger herself. The level of excitement in her voice was great
Premium Psychology Audience Attention
consecutive arithmetic progression terms as “d”‚ which is a common notation. Geometric Progressions (GP) A geometric progression is a list of terms as in an arithmetic progression but in this case the ratio of successive terms is a constant. In other words‚ each term is a constant times the term that immediately precedes it. Let us write the terms in a geometric progression as T1 ‚ T2 ‚ T3 and so on. An example of a geometric progression is 10; 100; 1000; 10000; Since the ratio of successive terms
Free Geometric progression Addition Summation