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Arithmetic series full chapter explanation |
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Answer» ong>Explanation: Arithmetic Progressions An Arithmetic Progression is a SEQUENCE of numbers in which we get each term by adding a particular number to the previous term, except the first term. Each number in the sequence is known as term. The fixed number i.e. the difference between each term with its preceding term is known as common difference. It can be positive, NEGATIVE or zero. It is represented as ‘d’. Some Examples of Arithmetic Progressions Common difference Value of d Example d > 0, positive 10 20, 30, 40, 50,… d < 0, negative -25 100, 75, 50, 25, 0 d = 0, zero 0 5, 5, 5, 5,.. General form of Arithmetic Progression General form of Arithmetic Progression Where the first term is ‘a’ and the common difference is ‘d’. Example Given sequence is 2, 5, 8, 11, 14,… Here, a = 2 and d = 3 d = 5 – 2 = 8 – 5 = 11 – 8 = 3 First term is a = 2 Second term is a + d = 2 + 3 = 5 Third term is a + 2d = 2 + 6 = 8 and so on. Finite or Infinite Arithmetic Progressions 1. Finite Arithmetic Progression If there are only a limited number of terms in the sequence then it is known as finite Arithmetic Progression. 0 Home» Revision Notes»Class 10 Maths»Arithmetic Progressions Revision Notes on Arithmetic Progressions Arithmetic Progressions An Arithmetic Progression is a sequence of numbers in which we get each term by adding a particular number to the previous term, except the first term. Arithmetic Progressions Each number in the sequence is known as term. The fixed number i.e. the difference between each term with its preceding term is known as common difference. It can be positive, negative or zero. It is represented as ‘d’. Some Examples of Arithmetic Progressions Common difference Value of d Example d > 0, positive 10 20, 30, 40, 50,… d < 0, negative -25 100, 75, 50, 25, 0 d = 0, zero 0 5, 5, 5, 5,.. General form of Arithmetic Progression General form of Arithmetic Progression Where the first term is ‘a’ and the common difference is ‘d’. Example Given sequence is 2, 5, 8, 11, 14,… Here, a = 2 and d = 3 d = 5 – 2 = 8 – 5 = 11 – 8 = 3 First term is a = 2 Second term is a + d = 2 + 3 = 5 Third term is a + 2d = 2 + 6 = 8 and so on. Finite or Infinite Arithmetic Progressions 1. Finite Arithmetic Progression If there are only a limited number of terms in the sequence then it is known as finite Arithmetic Progression. 229, 329, 429, 529, 629 2. Infinite Arithmetic Progression If there are an infinite number of terms in the sequence then it is known as infinite Arithmetic Progression. 2, 4, 6, 8, 10, 12, 14, 16, 18…..… The nth term of an Arithmetic Progression If an is the nth term,a1 is the first term, n is the number of terms in the sequence and d is a common difference then the nth term of an Arithmetic Progression will be The nth term of an Arithmetic Progression Example Find the 11th term of the AP: 24, 20, 16,… Solution Given a = 24, n = 11, d = 20 – 24 = – 4 an = a + (n - 1)d a11 = 24 + (11-1) – 4 = 24 + (10) – 4 =24 – 40 = -16 Arithmetic Series The arithmetic series is the sum of all the terms of the arithmetic sequence. The arithmetic series is in the form of {a + (a + d) + (a + 2d) + (a + 3d) + .........} Sum of first n terms of an Arithmetic series Sum of the first n terms of the sequence is CALCULATED by 229, 329, 429, 529, 629 2. Infinite Arithmetic Progression If there are an infinite number of terms in the sequence then it is known as infinite Arithmetic Progression. 2, 4, 6, 8, 10, 12, 14, 16, 18…..… The nth term of an Arithmetic Progression If an is the nth term,a1 is the first term, n is the number of terms in the sequence and d is a common difference then the nth term of an Arithmetic Progression will be |
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