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Arithmetic and Geometric Progression Video Lecture | Mathematics (Maths) for JEE Main & Advanced
FAQs on Arithmetic and Geometric Progression Video Lecture - Mathematics (Maths) for JEE Main & Advanced
| 1. What is the difference between an arithmetic progression (AP) and a geometric progression (GP)? |  |
Ans.An arithmetic progression (AP) is a sequence of numbers in which the difference between consecutive terms is constant, while a geometric progression (GP) is a sequence where the ratio between consecutive terms is constant. For example, in the AP 2, 5, 8, 11, the common difference is 3; in the GP 3, 6, 12, 24, the common ratio is 2.
| 2. How do you find the nth term of an arithmetic progression? | |
Ans.The nth term of an arithmetic progression can be found using 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 \( a = 2 \) and \( d = 3 \), the 5th term is \( a_5 = 2 + (5-1) \cdot 3 = 14 \).
| 3. How is the sum of the first n terms of an arithmetic progression calculated? | |
Ans.The sum of the first n terms of an arithmetic progression can be calculated using the formula: \( S_n = \frac{n}{2} \times (2a + (n-1)d) \) or \( S_n = \frac{n}{2} \times (a + l) \), where \( l \) is the last term. For example, for \( a = 2 \), \( d = 3 \), and \( n = 5 \), \( S_5 = \frac{5}{2} \times (2 \cdot 2 + (5-1) \cdot 3) = 40 \).
| 4. What is the formula for the nth term of a geometric progression? | |
Ans.The nth term of a geometric progression can be calculated using the formula: \( a_n = a \cdot r^{(n-1)} \), where \( a \) is the first term, \( r \) is the common ratio, and \( n \) is the term number. For instance, if \( a = 3 \) and \( r = 2 \), the 4th term is \( a_4 = 3 \cdot 2^{(4-1)} = 24 \).
| 5. How can you find the sum of the first n terms of a geometric progression? | |
Ans.The sum of the first n terms of a geometric progression can be calculated using the formula: \( S_n = a \frac{1 - r^n}{1 - r} \) (for \( r \neq 1 \)), where \( a \) is the first term and \( r \) is the common ratio. For example, for \( a = 3 \) and \( r = 2 \) with \( n = 4 \), \( S_4 = 3 \frac{1 - 2^4}{1 - 2} = 45 \).
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