Chapter 12.1, Problem 9CFU

To determine

To calculate: The $17\text{th}$ term of the arithmetic sequence for which first term is 10 and common difference is $-3$ .

Answer to Problem 9CFU

The $18\text{th}$ term of the arithmetic sequence is $-38$ .

Explanation of Solution

Given information:

The arithmetic sequence has first term as $a_1=10$ and common difference as $d=-3$ .

Formula used:

A sequence with first term as $a_1$ and next term written as sum of preceding term and common difference then it is called an arithmetic sequence. It is denoted as $a_1,a_1+d,a_1+2d+\dots$ .

The $n\text{th}$ term of the arithmetic sequence is $a_n=a_1+\left(n-1\right)d$ .

Calculation:

Consider the arithmetic sequence that has first term as $a_1=10$ and common difference as $d=-3$ .

Recall that a sequence with first term as $a_1$ and next term written as sum of preceding term and common difference then it is called an arithmetic sequence. It is denoted as $a_1,a_1+d,a_1+2d+\dots$ .

The $n\text{th}$ term of the arithmetic sequence is $a_n=a_1+\left(n-1\right)d$ .

Apply it, for the $17\text{th}$ term of the arithmetic sequence

  $\begin{array}{c}{a}_{17}=a_1+\left(17-1\right)d\\ =10+16\left(-3\right)\\ =-38\end{array}$

Thus, the $17\text{th}$ term of the arithmetic sequence is $-38$ .