Easy AP term

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#class10 • #Math • #class10math • #arithmetic progression • #satyamrfoundation • #srf • Arithmetic Progression (AP) is a sequence of numbers in which the difference between consecutive terms is constant. • Key Concepts: • 1. First Term (a): The initial term of the sequence. • 2. Common Difference (d): The constant difference between consecutive terms. • 3. Number of Terms (n): The total count of terms in the sequence. • AP Formula: • 1. General Term: an = a + (n-1)d • 2. Sum of n Terms: Sn = n/2 [2a + (n-1)d] • 3. Last Term: l = a + (n-1)d • Types of AP: • 1. Finite AP: Has a finite number of terms. • 2. Infinite AP: Has an infinite number of terms. • Examples: • 1. 2, 5, 8, 11, ... (a=2, d=3) • 2. 10, 15, 20, 25, ... (a=10, d=5) • Applications: • 1. Financial calculations (interest, investments) • 2. Physics (motion, velocity) • 3. Computer Science (algorithms, data structures) • 4. Statistics (data analysis) • Properties: • 1. The sum of an AP is equal to the average of the first and last terms multiplied by the number of terms. • 2. The average of an AP is equal to the sum of the first and last terms divided by 2. • Solved Example: • Find the 10th term and sum of the AP: 3, 7, 11, 15, ... • Solution: • a = 3, d = 4, n = 10 • 10th term: an = 3 + (10-1)4 = 3 + 36 = 39 • Sum: Sn = 10/2 [2(3) + (10-1)4] = 5(6 + 36) = 210

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