Chapter 11, Problem 5MCQ

To determine

To find the indicated terms of each arithmetic sequence

  $a_1=10,d=-5,n=9$

Answer to Problem 5MCQ

The indicated terms of each arithmetic sequence is -30.

Explanation of Solution

Given:

  $a_1=10,d=-5,n=9$

Concept Used:

  $n^{th}$ term of an arithmetic sequence with first term a and common term d is: $a_n=a_{\left(n-1\right)}+d$ .

Calculation:

In order to find the indicated terms of each arithmetic sequence

  $a_1=10,d=-5,n=9$

Use the formula for $n^{th}$ term of an arithmetic sequence with first term a and common term d is: $a_n=a+\left(n-1\right)d$ .

Here, given that first term is 10 and common difference is

  $d=-5$

To find the indicated terms of each arithmetic sequence $a_9$ , as

  $\begin{array}{c}{a}_n=a_1+\left(n-1\right)d\\ a_9=10+\left(9-1\right)\left(-5\right)\\ =10+8\left(-5\right)\\ =10-40\\ =-30\end{array}$

Thus, the indicated terms of each arithmetic sequence is -30.