Chapter 9, Problem 30CT

Solution

To write an arithmetic sequence and then write an explicit formula for it.

There can be many answers to this question. An example can be the arithmetic sequence $2,7,12,17,23,\mathrm{...}$ and its explicit formula is $a_n=5n-3$ .

Given information:

To write an arithmetic sequence.

Calculation:

An arithmetic sequence can be construction by writing a first term and choosing a common difference.

For example, consider an arithmetic sequence with $a_1=2$ and $d=5$ .

So, the sequence can be written as $2,7,12,17,23,\mathrm{...}$ .

Now, use the nth term formula $a_n=a_1+\left(n-1\right)d$ of an arithmetic sequence to write the explicit formula for this sequence.

  $\begin{array}{c}{a}_n=a_1+\left(n-1\right)d\\ =2+\left(n-1\right)\cdot 5\\ =2+5n-5\\ =5n-3\end{array}$

Conclusion:

An arithmetic sequence can be given as $2,7,12,17,23,\mathrm{...}$ and its explicit formula is $a_n=5n-3$.