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

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

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

1. 1. Introduction What do you observe in the following pictures? A certain pattern has been followed while creating these things.
2. 2. Some Number Patterns 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 7th,8th,9th and 10th 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.
3. 3. 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.
4. 4. Some Number Patterns The number of unit squares in a square with sides 1, 2, 3, 4, ... units are respectively 1, 4, 9, 16, .... Here we can observe that 1 = 12, 4 = 22, 9 = 32, 16 = 42, ... Here the succeeding terms are squares of consecutive numbers.
5. 5. Arithmetic Progressions Consider the following lists of numbers : 1, 3, 5, 7, 9, .... 10, 8, 6, 4, 2, .... – 3, –2, –1, 0, .... 5, 5, 5, 5, 5, .... 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 Each list follows a pattern or rule.
6. 6. Arithmetic Progressions 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.
7. 7. Formula for Common Difference Let us denote the first term of an AP by a1, second term by a2, . . ., nth term by an and the common difference by d. Then the AP becomes a1, a2, a3, . . ., an So, a2 - a1 = a3 - a2 = . . . = an - an - 1 = d an – an – 1 = d
8. 8. General Form of an AP 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.
9. 9. Finite and Infinite APs Finite AP • Number of students in class 5th to 10th are 25, 23, 21, 19, 17, 15. • There are only a finite number of terms. • They have a last term. Infinite AP • 2, 7, 12, 17, 22, .... • There are infinite number of terms. • They do not have a last term.
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