Arithmetic Progression: Common Difference and Nth Term

Arithmetic Progression

Common Difference (d)

• The common difference is the constant difference between consecutive terms in an arithmetic progression.
• It is denoted by the symbol 'd'.
• d = a2 - a1 = a3 - a2 = ... = an - an-1, where 'a' represents the terms in the AP.

Nth Term (an)

• The nth term of an arithmetic progression can be found using the formula: an = a1 + (n - 1)d, where 'a1' is the first term and 'n' is the term number.
• This formula allows us to find any term in the progression.

Sum of Terms (Sn)

• The sum of the first 'n' terms of an arithmetic progression can be found using the formula: Sn = (n/2) × (a1 + an), where 'a1' is the first term and 'an' is the last term.
• This formula can be used to find the sum of any number of terms in the progression.
• When the number of terms is even, the sum can be found by taking the average of the first and last terms and multiplying by the number of terms.
• When the number of terms is odd, the sum can be found by taking the average of the first and last terms, multiplying by the number of terms, and adding the middle term.

Arithmetic Progression

Common Difference (d)

• d is the constant difference between consecutive terms in an AP
• d is denoted by the symbol 'd'
• d = a2 - a1 = a3 - a2 = ... = an - an-1, where 'a' represents the terms in the AP

Nth Term (an)

• The nth term of an AP can be found using the formula: an = a1 + (n - 1)d
• a1 is the first term and 'n' is the term number
• This formula allows us to find any term in the progression

Sum of Terms (Sn)

• The sum of the first 'n' terms of an AP can be found using the formula: Sn = (n/2) × (a1 + an)
• a1 is the first term and 'an' is the last term
• When the number of terms is even, the sum can be found by taking the average of the first and last terms and multiplying by the number of terms
• When the number of terms is odd, the sum can be found by taking the average of the first and last terms, multiplying by the number of terms, and adding the middle term

Learn about the common difference and nth term of an arithmetic progression, including formulas and definitions.