N:B: In this case we apply multiplication or division.Ī.P-G.P SERIES: The series in which we get the next term first by adding/subtracting and then with that result by multiplying/dividing, is known as A.P-G.P series.e.g. GEOMETRIC SERIES: The series in which the ratio between each successive terms is constant, is known as geometric series.e.g.1,3,9,27,81,243,729 etc. In this case after first step, the differences are 126,90,60,36,18,6.After second step, the differences of these differences are 36,30,24,18,12.After third step ,the differences are 6,6,6,6…. Three tier Arithmetic Series: The series in which the difference is constant after three steps, is known as Three-tier Arithmetic series.e.g.336,210,120,60,24,6,0etc. In this series, after first step the difference are 4,6,8,10,12,14,16,18,20.And, after second step the differences are 2,2,2,2,2,2etc in all the cases. Two tier Arithmetic series: The series in which the difference is constant after two steps, is known as Two tier Arithmetic series.e.g.2,6,12,20,30,42,56,72,90,120 etc. SQUARE SERIES: The series in which all the numbers are squares of natural numbers followed by a sequence is known as square series.e.g.1,4,9,16,25,36,49,64,81,100,121etc.ĬUBE SERIES: The series in which all the numbers are the cube of natural numbers followed by a sequence, is known as cube series. PRIME SERIES: The series in which all the numbers are prime numbers followed by a sequence, is known as prime series.e.g.2,3,5,7,11,13,17,19,23,29,31 etc. ODD SERIES: The series in which all the numbers are odd numbers followed by a sequence, is known as odd series. TYPES OF SERIESEVEN SERIES: The series in which all the numbers are even numbers followed by a sequence ,is known as even series. Such as:Find the next term in single line series.(ii) Find the odd term in single line series.(iii) Find out the value in two line series. Find out how here.INTRODUCTION:A sequence of numbers is known as number series.There are three types of questions coming. Some people think this is one of the reasons it sounds so good.Īs well as being used to craft violins, the Golden Ratio that comes from the Fibonacci Sequence is also used for saxophone mouthpieces, in speaker wires, and even in the acoustic design of some cathedrals.Įven Lady Gaga has used it in her music. The Golden Ratio can be found throughout the violin by dividing lengths of specific parts of the violin. Stradivari used the Fibonacci Sequence and the Golden Ratio to make his violins. There's a reason a Stradivarius violin would cost you a few million pounds to buy – and its value is partly down to the Fibonacci Sequence and its Golden Ratio. Read more: To save the sound of a Stradivarius, this entire Italian city is keeping quiet Hailed as the master of violin making, Antonio Stradivari has made some of the most beautiful and sonorous violins in existence. The first movement as a whole consists of 100 bars.Ħ2 divided by 38 equals 1.63 (approximately the Golden Ratio)Įxperts claim that Beethoven, Bartók, Debussy, Schubert, Bach and Satie (to name a few) also used this technique to write their sonatas, but no one is exactly sure why it works so well. The exposition consists of 38 bars and the development and recapitulation consists of 62. In the above diagram, C is the sonata's first movement as a whole, B is the development and recapitulation, and A is the exposition. The Golden Ratio in Mozart's Piano Sonata No. Let's take the first movement of Mozart's Piano Sonata No. Mozart arranged his piano sonatas so that the number of bars in the development and recapitulation divided by the number of bars in the exposition would equal approximately 1.618, the Golden Ratio.
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