Question

A sequence is _______
A term is ________ a finite sequence is _______while infinite sequence is ______ to find the specifiwd term/s of a sequence when given the general term, ______ to write the general term of a sequence when given some terms, ______​

Answer 1

Answer:

Sequence

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

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

In the sequence, each number is called a term. The number 5 has first position, 15 has second position, 25 has third position and so on.

The nth term of a sequence is sometimes written an .

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 nth term an can be calculated using the equation an=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}

The first of the sequence is 4 and the last term is 64 . Since the sequence has a last term, it is a finite sequence.

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

The first term of the sequence is 4 . The "..." at the end indicates that the sequence goes on forever; it does not have a last term. It is an infinite sequence.

Increasing and Decreasing Sequences

An increasing sequence is one in which every term is greater than the previous term. That is, an+1>an .

The following two sequences are both increasing.

{5,7,9,11,13,15,…}

{1,1.5,1.75,1.825,1.9375,…}

A decreasing sequence is one in which every term is greater than the previous term. That is, an+1<an .

The following two sequences are both decreasing.

{100,50,0,−50,−100,−150,−200,…}

{1,0.5,0.25,0.125,0.0625,…}

It is possible for a sequence to be neither increasing nor decreasing:

{0,1,−2,3,−4,5,−6,7,…}

Arithmetic and Geometric Sequences

An arithmetic sequence is a sequence in which the difference between any two consecutive terms is the same.

Example: 10,20,30,40,50,…

Here, the common difference between any two consecutive terms is 10 .

A geometric sequence is a sequence in which the common ratio between any two consecutive terms is the same.

Example: 2,8,32,128,512,…

Here, the common ratio between any two consecutive terms is 4 .