Arithmetic progression - Introduction to Arithmetic progressions for class 10 maths.

Arithmetic progression - Introduction to Arithmetic progressions for class 10 maths.

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1. Arithmetic Progressions

2. Introduction What do you observe in the following pictures? A certain pattern has been followed while creating these things.

3. Namita’s school offered her a scholarship of Rs. 1000 when she was in class 6 and increased the amount by Rs. 500 each year till class 10. The amounts of money (in Rs ) Namita received in class 7 th ,8 th ,9 th and 10 th were respectively : 1500, 2000, 2500 and 3000 Each of the numbers in the list is called a term. Here we find that the succeeding terms are obtained by adding a fixed number. Some Number Patterns

4. Some Number Patterns In a savings scheme, the amount becomes double after every 10 years. The maturity amount (in Rs) of an investment of Rs 8000 after 10, 20, 30 and 40 years will be, respectively: 16000, 32000, 64000, 128000 Here we find that the succeeding terms are obtained by multiplying with a fixed number.

5. The number of unit squares in a square with sides 1, 2, 3, 4, ... units are respectively 1 , 4, 9, 16, .... Some Number Patterns Here we can observe that 1 = 1 2 , 4 = 2 2 , 9 = 3 2 , 16 = 4 2 , ... Here the succeeding terms are squares of consecutive numbers.

6. Consider the following lists of numbers : Arithmetic Progressions 1, 3, 5, 7, 9, .... 10, 8, 6, 4, 2, .... – 3, –2, –1, 0, .... 5, 5, 5, 5, 5, .... Each list follows a pattern or rule . each term is obtained by adding 2 to the previous term each term is obtained by adding - 2 to the previous term each term is obtained by adding 1 to the previous term each term is obtained by adding 0 to the previous term

7. An arithmetic progression (AP) is a list of numbers in which each term is obtained by adding a fixed number to the previous term except the first term. This fixed number is called the common difference of the AP. It can be positive, negative or zero. Arithmetic Progressions

8. a n – a n – 1 = d Let us denote the first term of an AP by a 1 , second term by a 2 , . . ., nth term by a n and the common difference by d . Then the AP becomes a 1 , a 2 , a 3 , . . ., a n Formula for Common Difference a 3 - So, a 1 = a 2 - a 2 = . . . a n = - a n - 1 = d

9. We can see that a, a + d, a + 2d, a + 3d, . . . represents an arithmetic progression where a is the first term and d the common difference. This is called the general form of an AP. General Form of an AP

10. Finite and Infinite APs

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