Chapter SH, Problem 10.5EP

To determine

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

Answer to Problem 10.5EP

The equation for the nth term of the given arithmetic sequence is $a_n=3-15\left(n-1\right)$ .

Explanation of Solution

Given:

The given sequence is $3,-12,-27,\mathrm{...}$ .

Calculation:

Find the common difference as follows.

  $\begin{array}{c}-12-3=-15\\ -27+12=-15\\ ⋮\end{array}$

Substitute 3 for $a$ , and $-15$ 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.

  $\begin{array}{c}{a}_n=3+\left(n-1\right)\left(-15\right)\\ a_n=3-15\left(n-1\right)\end{array}$

Therefore, the equation for the nth term of the given arithmetic sequence is $a_n=3-15\left(n-1\right)$ .