Sequences and Series — Chapter Summary

A sequence is an arrangement

A sequence is an arrangement of numbers in a definite order according to some rule. It can also be regarded as a function whose domain is the set of n

The nth term of a sequence

The nth term of a sequence is the number at the nth position and is denoted by an. It is also called the general term of the sequence. For even natura

A finite sequence has a fixed

A finite sequence has a fixed number of terms. An infinite sequence does not end. The sequence of ancestors over ten generations is finite, while the

A series is the expression a1

A series is the expression a1 + a2 + a3 + ... formed by adding the terms of a sequence. Sigma notation writes this compactly as Σ from k = 1 to n of a

A sequence a1

A sequence a1, a2, a3, ... is a geometric progression if each term is non-zero and the ratio a(k+1)/ak is constant. If the first term is a and common