Chapter 12.1, Problem 3E

To determine

Calculate the first four and the $100th$ term of the given sequence.

Answer to Problem 3E

The first four term of the sequence are $2,3,4,5$ and the $100th$ term are $101$ .

Explanation of Solution

Given:

It is given in the question that the sequence is $a_n=n+1$ .

Concept Used:

In this, use the concept of arithmetic progression in which put the number and calculate the problem.

Calculation:

Here, the sequence is $a_n=n+1$ .

To find the first four terms, substitute $n=1,2,3and4$ in the formula for the nth term

  $a_n=n+1$ ( nth term)

  $\begin{array}{l}{a}_1=1+1=2(n=1)\\ a_2=2+1=3(n=2)\\ a_3=3+1=4(n=3)\\ a_4=4+1=5(n=4)\end{array}$

Now, to find the $100th$ term, substitute $n=100$ ,

  $a_{100}=100+1=101$

Conclusion:

The first four term of the sequence are $2,3,4,5$ and the $100th$ term are $101$ .