Chapter 8, Problem 7MCQ

To determine

To calculate: To describe the sequence using words and symbols

Answer to Problem 7MCQ

Sequence is given by equation $t=1+2n$

Explanation of Solution

Given information:Sequence is $3,5,7,9,\mathrm{....}$

Formula Used:

Term: In a sequence, each number is referred to as a term

Term Number: In a sequence, the position of the given term is referred to as term number.

When the difference between the consecutive terms of a sequence is common, then the sequence is an arithmetic sequence.

Nth number of arithmetic sequence is given as

  $t_n=a+\left(n-1\right)d$

Calculation:

Sequence is given as follow:

  $3,5,7,9,\mathrm{....}$

Here, the first term of the sequence is $a=3$

Also, the common difference is

  $d=5-3=7-5=2$

Since the difference is common, hence the sequence in arithmetic sequence.

Let term is denoted by $t$ and term number is denoted as $n$

Thus, nth term of arithmetic sequence is given as

  $t=a+\left(n-1\right)d$

Substituting the values in above equation,

  $\begin{array}{l}t=3+\left(n-1\right)2\\ t=3+2n-2\\ t=1+2n\end{array}$

Also, in words, term is more than twice the term number.

Conclusion:

Hence, sequence is given by equation $t=1+2n$