Chapter 12, Problem 1RCC

a.

To determine

Explain the meaning of sequence.

Answer to Problem 1RCC

A sequence is an enumerated collection of objects in which repetitions are allowed and order does matter, for example there are many types of sequence like arithmetic and geometric.

Explanation of Solution

Given information:

It is given in the question that, define the meaning of sequence.

A sequence is an enumerated collection of objects in which repetitions are allowed and order does matter, for example there are many types of sequence like arithmetic and geometric.

b.

To determine

Explain the meaning of an arithmetic sequence and also write the expression for the $nth$ term of sequence.

Answer to Problem 1RCC

An arithmetic sequence is a sequence of the numbers such that the difference between the consecutive terms is constant and the expression for the $nth$ term of sequence is $a_n=a+\left(n-1\right)d$

Where,

  $\begin{array}{l}{a}_{n}isthenthterm\\ aisthefirstterm\\ nisthenumberofterm\\ disthecommandifference\end{array}$

Explanation of Solution

Given information:

It is given in the question that, to explain the meaning of arithmetic sequence and also write the expression for the $nth$ term of arithmetic sequence.

An arithmetic sequence is a sequence of the numbers such that the difference between the consecutive terms is constant and the expression for the $nth$ term of arithmetic sequence is $a_n=a+\left(n-1\right)d$

Where,

  $\begin{array}{l}{a}_{n}isthenthterm\\ aisthefirstterm\\ nisthenumberofterm\\ disthecommandifference\end{array}$

c.

To determine

Explain the meaning of geometric sequence and also write the expression for the $nth$ term of geometric sequence.

Answer to Problem 1RCC

A geometric sequence is a sequence of the numbers such that the difference ratio of the two consecutive terms is constant and the expression for the $nth$ term of geometric sequence is $a_n=a{r}^{n-1}$

Where,

  $\begin{array}{l}{a}_{n}isthenthterm\\ aisthefirstterm\\ nisthenumberofterm\\ risthecommanratio\end{array}$

Explanation of Solution

Given information:

It is given in the question that, to explain the meaning of geometric sequence and also write the expression for the $nth$ term of geometric sequence.

A geometric sequence is a sequence of the numbers such that the difference ratio of the two consecutive terms is constant and the expression for the $nth$ term of geometric sequence is $a_n=a{r}^{n-1}$

Where,

  $\begin{array}{l}{a}_{n}isthenthterm\\ aisthefirstterm\\ nisthenumberofterm\\ risthecommanratio\end{array}$