General Term ( n th term) of an Arithmetic Sequence The general term of an arithmetic sequence with first term a 1 and the common difference d is a n = a 1 + ( n - 1 ) d Sum of the First n Terms of an Arithmetic Sequence The sum, S n , of the first n terms of an arithmetic sequence, where a 1 is the first term and a n is the n th term is S n = n 2 ( a 1 + a n )

General Term ( n th term) of a Geometric Sequence: The general term of a geometric sequence with first term a 1 and the common ratio r is a n = a 1 r n - 1 Sum of the First n Terms of a Geometric Series: The sum, S n , of the n terms of a geometric sequence is S n = a 1 ( 1 - r n ) 1 - r where a 1 is the first term and r is the common ratio

sequence — A sequence is a function whose domain is the counting numbers. common difference — The difference between consecutive terms in an arithmetic sequence, a n - 1 , is d , the common difference, for n greater than or equal to two. common ratio — The ratio between consecutive terms in a geometric sequence, a n - 1 , is r , the common ratio, where n is greater than or equal to two. arithmetic sequence — An arithmetic sequence is a sequence where the difference between consecutive terms is constant.