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Page 1 1 1 6 6 5 5 8 8 4 4 9 9 3 3 7 7 2 2 0 0 A r i t h m e t i c P r o g r e s s i o n s Page 2 1 1 6 6 5 5 8 8 4 4 9 9 3 3 7 7 2 2 0 0 A r i t h m e t i c P r o g r e s s i o n s + 1 + 2 + 3 1 2 3 4 5 6 7 8 9 1 0 1 1 Suppose a boy takes one step Next, the boy takes two step Next, he takes three steps How many steps would he take next? Page 3 1 1 6 6 5 5 8 8 4 4 9 9 3 3 7 7 2 2 0 0 A r i t h m e t i c P r o g r e s s i o n s + 1 + 2 + 3 1 2 3 4 5 6 7 8 9 1 0 1 1 Suppose a boy takes one step Next, the boy takes two step Next, he takes three steps How many steps would he take next? + 1 + 2 + 3 + 4 1 2 3 4 5 6 7 8 9 1 0 1 1 4 right? Page 4 1 1 6 6 5 5 8 8 4 4 9 9 3 3 7 7 2 2 0 0 A r i t h m e t i c P r o g r e s s i o n s + 1 + 2 + 3 1 2 3 4 5 6 7 8 9 1 0 1 1 Suppose a boy takes one step Next, the boy takes two step Next, he takes three steps How many steps would he take next? + 1 + 2 + 3 + 4 1 2 3 4 5 6 7 8 9 1 0 1 1 4 right? + 1 + 2 + 3 + 4 1 2 3 4 5 6 7 8 9 1 0 1 1 You observed the pattern and you could tell that the number of steps taken were increasing by 1 in every move. Page 5 1 1 6 6 5 5 8 8 4 4 9 9 3 3 7 7 2 2 0 0 A r i t h m e t i c P r o g r e s s i o n s + 1 + 2 + 3 1 2 3 4 5 6 7 8 9 1 0 1 1 Suppose a boy takes one step Next, the boy takes two step Next, he takes three steps How many steps would he take next? + 1 + 2 + 3 + 4 1 2 3 4 5 6 7 8 9 1 0 1 1 4 right? + 1 + 2 + 3 + 4 1 2 3 4 5 6 7 8 9 1 0 1 1 You observed the pattern and you could tell that the number of steps taken were increasing by 1 in every move. + 1 + 2 + 3 + 4 1 2 3 4 5 6 7 8 9 1 0 1 1 S e q u e n c e If we write the number of the stairs we moved on, we get: A Sequence is a group of number that follow some patternRead More
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FAQs on PPT: Arithmetic Progressions - Mathematics (Maths) Class 10
| 1. What is an arithmetic progression? |  |
Ans.An arithmetic progression (AP) is a sequence of numbers in which the difference between consecutive terms is constant. This difference is known as the common difference. For example, in the sequence 2, 5, 8, 11, the common difference is 3, as each term increases by 3.
| 2. How do you find the nth term of an arithmetic progression? | |
Ans.To find the nth term of an arithmetic progression, you can use the formula: aₙ = a₁ + (n - 1)d, where aₙ is the nth term, a₁ is the first term, n is the term number, and d is the common difference. This formula allows you to calculate any term in the sequence based on the first term and the common difference.
| 3. What is the formula for the sum of the first n terms of an arithmetic progression? | |
Ans.The formula for the sum of the first n terms (Sₙ) of an arithmetic progression is Sₙ = n/2 * (2a₁ + (n - 1)d), where Sₙ is the sum of the first n terms, a₁ is the first term, n is the number of terms, and d is the common difference. Alternatively, it can also be expressed as Sₙ = n/2 * (a₁ + aₙ), where aₙ is the nth term.
| 4. Can an arithmetic progression have a negative common difference? | |
Ans.Yes, an arithmetic progression can have a negative common difference. When the common difference is negative, the terms of the sequence will decrease. For example, in the sequence 10, 7, 4, 1, the common difference is -3, indicating a decreasing pattern.
| 5. How can you identify if a given sequence is an arithmetic progression? | |
Ans.To identify if a given sequence is an arithmetic progression, check if the difference between consecutive terms is constant. If you subtract each term from the next and find that the differences are equal, then the sequence is an arithmetic progression. For instance, in the sequence 4, 8, 12, 16, the differences (4, 4, 4) are constant, confirming it is an AP.
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