Arithmetic Progression Formulas

Arithmetic Progression

Common Difference (d)

• The common difference is the difference between any two consecutive terms in an arithmetic progression.
• It is denoted by the symbol 'd'.
• The common difference is constant for an arithmetic progression.
• Formula: d = an - an-1, where an is a term in the sequence and an-1 is the preceding term.

Nth Term (an)

• The nth term of an arithmetic progression is given by the formula: an = a1 + (n-1)d
• Where:
  • an is the nth term
  • a1 is the first term
  • n is the term number (starting from 1)
  • d is the common difference

Sum of Terms (Sn)

• The sum of the first 'n' terms of an arithmetic progression is given by the formula: Sn = (n/2)(a1 + an)
• Where:
  • Sn is the sum of the first 'n' terms
  • a1 is the first term
  • an is the nth term
• This formula is known as the formula for the sum of an arithmetic series.

Arithmetic Progression

Common Difference (d)

• Common difference (d) is the difference between any two consecutive terms in an arithmetic progression.
• The symbol 'd' denotes the common difference.
• The common difference is constant in an arithmetic progression.
• The formula to find the common difference is d = an - an-1, where an is a term in the sequence and an-1 is the preceding term.

Nth Term (an)

• The formula to find the nth term of an arithmetic progression is an = a1 + (n-1)d.
• In this formula, an is the nth term, a1 is the first term, n is the term number (starting from 1), and d is the common difference.

Sum of Terms (Sn)

• The formula to find the sum of the first 'n' terms of an arithmetic progression is Sn = (n/2)(a1 + an).
• In this formula, Sn is the sum of the first 'n' terms, a1 is the first term, and an is the nth term.
• This formula is known as the formula for the sum of an arithmetic series.