Question

relation between any two terms of sequence

Answer 1

A sequence is a list of numbers in a certain order. Each number in a sequence is called aterm . Each term in a sequence has a position (first, second, third and so on).

For example, consider the sequence{5,15,25,35,…}{5,15,25,35,…}

In the sequence, each number is called a term. The number 55 has first position, 1515 has second position, 2525 has third position and so on.

The nthnth term of a sequence is sometimes written anan .

Often, you can find an algebraic expression to represent the relationship between any term in a sequence and its position in the sequence.

In the above sequence, the nthnth term anan can be calculated using the equationan=10n−5an=10n−5 .

Finite and Infinite Sequences

A sequence is finite if it has a limited number of terms and infinite if it does not.

Finite sequence: {4,8,12,16,…,64}{4,8,12,16,…,64}

The first of the sequence is 44 and the last term is 6464 . Since the sequence has a last term, it is a finite sequence.

Infinite sequence: {4,8,12,16,20,24,…}{4,8,12,16,20,24,…}

The first term of the sequence is 44 . The "..." at the end indicates that the sequence goes on forever; it does not have a last term. It is an infinite sequence.