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Arithmetic Progression And Geometric Progression With Examples (AP & GP) |

This presentation covers the fundamentals of arithmetic progression and geometric progression. It explains how to calculate the nth term of a sequence and the sum of the n terms. There are also a few numerical problems.

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Arithmetic Progression And Geometric Progression With Examples (AP & GP) |

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  1. What’s in it for you? Arithmetic Progression Nth Term and Sum of N Terms Arithmetic Progression Example Geometric Progression Geometric Progression Example

  2. Arithmetic Progression

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  4. Arithmetic Progression 2, 4, 6, 8, 10 The sequence is an example of A.P. In this, each term is obtained by adding 2 to the preceding term If various terms of a sequence are formed by adding a fixed number to the previous term or the difference between the two successive terms is constant, then the sequence is called an A.P

  5. nth Term and Sum of n Terms The nth term of a A.P with first term ‘a’ and common difference ‘d’ is given by The sum of n terms of a A.P with first term ‘a’ and common difference ‘d’ is given by an = a + (n-1)d Sn = n/2 [2a + (n-1)d] an = nth term a = first term d = common difference Sn = Sum of n terms a = first term d = common difference

  6. Arithmetic Progression Example For the series 2, 6, 10, 14, …… Find the 12th term Sum of the first 12 terms of the series For the series, we have a = 2, d = 4 Using an  = a + (n-1)d a12  = 2 + (12-1)4 = 46 b) Using Sn = n/2 [2a + (n-1)d] S12 = 12/2 [2*2 + (12-1)4] = 288

  7. Geometric Progression

  8. Geometric Progression If the first term is denoted by a, and the common ration by r, the series can be written as: a + ar2 + ar3 + …. A Geometric Progression or Geometric Series is one in which each term is found by multiplying the previous term by a fixed number (common ratio)

  9. nth Term and Sum of n Terms The sum n terms of a G.P. with first term ‘a’ and common ratio ‘r’ is given by The nth term of a G.P. with first term ‘a’ and common ratio ‘r’ is given by an = arn-1 Sn = a[(rn-1)/(r-1)] an = nth term a = first term r = common ratio Sn = nth term a = first term r = common ratio

  10. Geometric Progression Example For the series 2 + 6 + 18 + 54 + ….. Find the 10th term b) The sum of the first 8 terms For the series, we have a = 2, r = 3 Using an = arn-1 a10 = 2(39) = 39366 b) Using Sn = a[(rn-1)/(r-1)] S8 = 2[(38-1)/(3-1)] = 6560

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