AP

Описание: #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