Chapter 12.1, Problem 18E

To determine

Calculate the first five term of the given sequence.

Answer to Problem 18E

The first five term of the sequence are $1,1,1,3,5$ .

Explanation of Solution

Given:

It is given in the question that the sequence is $a_n=a_{n-1}+a_{n-2}+a_{n-3}and{a}_1=a_2=a_3=1$ .

Concept Used:

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

Calculation:

Here, the sequence is $a_n=a_{n-1}+a_{n-2}+a_{n-3}and{a}_1=a_2=a_3=1$ .

Next, find $a_4$ ,

  $\begin{array}{l}{a}_n=a_{n-1}+a_{n-2}+a_{n-3}\left\{nthterm\right\}\\ a_4=a_{4-1}+a_{4-2}+a_{4-3}\{n=4\}\\ a_4=a_3+a_2+a_1\{a_1=a_2=a_3=1\}\\ a_4=1+1+1\\ a_4=3\end{array}$

Finally find $a_5$ ,

  $\begin{array}{l}{a}_n=a_{n-1}+a_{n-2}+a_{n-3}\left\{nthterm\right\}\\ a_5=a_{5-1}+a_{5-2}+a_{5-3}\{n=4\}\\ a_5=a_4+a_3+a_2\{a_2=a_3=1,a_4=3\}\\ a_5=3+1+1\\ a_5=5\end{array}$

Conclusion:

The first five term of the sequence are $1,1,1,3,5$ .