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FAQs on Mind Map: Arithmetic Progressions-2 - Mathematics (Maths) Class 10
| 1. What is an arithmetic progression (AP)? |  |
Ans.An arithmetic progression (AP) is a sequence of numbers in which the difference between any two 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.
| 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: \( a_n = a + (n-1)d \), where \( a \) is the first term, \( d \) is the common difference, and \( n \) is the term number. For example, if the first term is 2 and the common difference is 3, the 5th term would be \( a_5 = 2 + (5-1)3 = 14 \).
| 3. What is the sum of the first n terms of an arithmetic progression? | |
Ans.The sum of the first n terms of an arithmetic progression can be calculated using the formula: \( S_n = \frac{n}{2} (2a + (n-1)d) \) or \( S_n = \frac{n}{2} (a + l) \), where \( l \) is the last term. For example, if the first term is 2, common difference is 3, and you want to find the sum of the first 5 terms, it would be \( S_5 = \frac{5}{2} (2 \times 2 + (5-1) \times 3) = 40 \).
| 4. Can an arithmetic progression have a negative common difference? | |
Ans.Yes, an arithmetic progression can have a negative common difference. This would result in a decreasing sequence. For example, in the sequence 10, 7, 4, 1, the common difference is -3, demonstrating a valid arithmetic progression with a negative common difference.
| 5. How do you determine if a sequence is an arithmetic progression? | |
Ans.To determine if a sequence is an arithmetic progression, you can check if the difference between consecutive terms is constant throughout the sequence. If the difference remains the same for all pairs of consecutive terms, then the sequence is an arithmetic progression. For example, for the sequence 4, 8, 12, 16, the differences (4, 4, 4) are all equal, confirming it is an AP.
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