Arithmetic Progression: Common Difference and Nth Term

Study Notes

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.

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.

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.

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

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