Chapter 8, Problem 12MCQ

To determine

To calculate: To write an expression to find the value of the term in the $n^{th}$ position

Answer to Problem 12MCQ

Equation find the value of the term in the $n^{th}$ position is $t_n=9n-4$

Explanation of Solution

Given information:Table is

Position	1	2	3	4	n
Value	5	14	23	32

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:

Table is given as follows:

Position	1	2	3	4	n
Value	5	14	23	32

Sequence is given as follow:

  $5,14,23,32,\mathrm{...}$

Let the nth number be $t_n$

Here, the first term of the sequence is $a=5$

Also, the common difference is

  $d=14-5=23-14=9$

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

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

Thus, nth term of arithmetic sequence is given as

  $t_n=a+\left(n-1\right)d$

Substituting the values in above equation,

  $\begin{array}{l}{t}_n=5+\left(n-1\right)9\\ t_n=5+9n-9\\ t_n=9n-4\end{array}$

Conclusion:

Hence, the equation find the value of the term in the $n^{th}$ position is $t_n=9n-4$