Q. 5 - Calculus

Question

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

Step-by-Step Solution

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 $\{ 0,1,2,3,... \}$.

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 is $\{ 0,1,2,3,... \}$.

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