Question

What is meant by the index of a term of a sequence?

Short answer

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

The subscript of the terms of the sequence is $\{0,1,2,3,...\}$.

Hence, the index of the term of the sequence is $\{0,1,2,3,...\}$.

Step-by-step solution

Step1. Given Information.

given,

What is meant by the index of a term of a sequence?

Step2. The objective is to explain the index of terms of the sequence.

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

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

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

Step 3. Therefore,

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

The subscript of the terms of the sequence islocalid="1649307016389" $\{0,1,2,3,...\}$.

Hence, the index of the term of the sequence is $\{0,1,2,3,...\}$.