Q. 4 - Calculus

Question

What is a term of a sequence? 

Step-by-Step Solution

Answer

Each number in the sequence is called a term. 

Step1. Given Information

Consider the sequence.

The objective is to explain the term of sequence.

If k is the index of the sequence $\left\{a_k\right\}$ where k is a positive integer, the output $a_k$ is the term of the sequence.

Step2. Explanation

Let $a_k$ be the sequence defined as ${\left\{(-1{)}^{k}k\right\}}_{k=0}^{\mathrm{\infty }}.$

The term of the sequence can be found by substituting k=0,1,2,..

Sep3. Given Information

Therefore, $a_0=0,a_1=-1,a_2=2,a_3=-3,\dots$

Hence, the terms of the sequence are $\{0,-1,2,-3,\dots \}$.