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Presentation On Arithematic Progressions

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Published in: Mathematics
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Arithematic progressions

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  1. AritF,metic Progressions
  2. Introduction What do you observe in the following pictures? A certain pattern has been followed while cre things.
  3. Some Number Patterns Namita's school offered her a scholarship of Rs. 1000 when she was n class 6 and increase the amount by Rs. 500 each y ar till class -10. The amounts of money (in Rs) Namita eceived in class7th 8th 9th and 10th were respectively: 1500, 2000, 2500 and 3000 Each of the numb rs In e IS IS alled a term. Here we find that t adding a fixed number. erms are o
  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; .90 and 40 years will be, respectively: 16000, 3200076400 , 128000 Here we find that the terms are obtaine y multiplying with a fixed number.
  5. Some Number Patterns The number of unit squares in a square with sides I, 2, 3, 4, ... units are respectively I, 4, 9, 16, . Here we can observe that 12, 22, 32, 16 = 42 Here the succeeding terms are squares of co numbers. u iv
  6. Arithmetic Progressions Consider the following lists of numbers . 10, 8, each terrn is obtained previous term each terrn is obtained previous term each terro is obtained previous term each term is obtained previous terrn by by by by adding 2 to the adding - 2 to the adding 1 to the adding O to the Each list follows a pattern or rule.
  7. 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 the AP. It can be positive, negative or zero.
  8. Formula for Common Difference Let us denote the first term of an AP by a 1 , second term by ap nth term by an and the common difference by d. So, Then the AP becomes a 2 - a 1 = 03 -a
  9. General Form of an AP We can see that , 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.
  10. 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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