Chapter 8, Problem 11MCQ

To determine

To calculate: To write an equation that describes the sequence $7,12,17,22,\mathrm{...}$ and then find the 20^thterm of the sequence.

Answer to Problem 11MCQ

Equation that describes the sequence is $t=2+5n$ and the 20^thterm of sequence is $102$

Explanation of Solution

Given information:Sequence is $7,12,17,22,\mathrm{...}$

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:

  $7,12,17,22,\mathrm{...}$

Here, the first term of the sequence is $a=7$

Also, the common difference is

  $d=12-7=17-12=5$

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,

  $\begin{array}{l}t=7+\left(n-1\right)5\\ t=7+5n-5\\ t=2+5n\end{array}$

Also, 20^thterm of sequence is calculated as follows:

  $\begin{array}{l}{t}_{20}=2+\left(5\right)20\\ t_{20}=2+100\\ t_{20}=102\end{array}$

Conclusion:

Hence, the equation that describes the sequence is $t=2+5n$ and the 30^thterm of sequence is $102$