Chapter SH, Problem 10.6EP

To determine

To write: The equation for the nth term of the given arithmetic sequence.

Answer to Problem 10.6EP

The equation for the nth term of the given arithmetic sequence is $a_n=6+7\left(n-1\right)$ .

Explanation of Solution

Given:

The given sequence is $6,13,20,\mathrm{...}$ .

Calculation:

Find the common difference as follows.

  $\begin{array}{c}13-6=7\\ 20-13=7\\ ⋮\end{array}$

Substitute 6 for $a$ , and 7 for $d$ in the equation $a_n=a+\left(n-1\right)d$ to find the equation for the nth term for the arithmetic sequence.

  $\begin{array}{c}{a}_n=6+\left(n-1\right)\left(7\right)\\ a_n=6+7\left(n-1\right)\end{array}$

Therefore, the equation for the nth term of the given arithmetic sequence is $a_n=6+7\left(n-1\right)$ .