Foundational Concepts of Arithmetic Progression (AP)

by

Arithmetic Progression (AP):

  • Definition: An arithmetic progression is a sequence of numbers where the difference between consecutive terms remains constant. This constant difference is known as the common difference (d).
  • Example: 2, 5, 8, 11, 14…
  • Common Difference (d): In this example, the common difference is 3, as each term is obtained by adding 3 to the previous term.
  • General Term: The nth term of an arithmetic progression can be calculated using the formula: Tn = a + (n-1)d where:
    • Tn is the nth term
    • a is the first term
    • n is the position of the term in the sequence
    • d is the common difference
  • Sum of n terms: The sum of the first n terms of an arithmetic progression can be calculated using the formula: Sn = n/2 * (2a + (n-1)d) or Sn = n/2 * (a + l) where:
    • Sn is the sum of the first n terms
    • a is the first term
    • n is the number of terms
    • d is the common difference
    • l is the last term