Chapter 8.1, Problem 57E

To determine

To write: the first five terms of the sequence defined recursively.

Answer to Problem 57E

The first five terms are

  $3,4,6,10,18$ .

Explanation of Solution

Given information:

Given sequence

  $a_0=1,a_1=3,a_k=a_{k-2}+a_{k-1}$

Calculation:

Since the first term of the sequence is $a_0=1,a_1=3$ therefore, the subsequent terms can be computed from the recursive formula, $a_k=a_{k-2}+a_{k-1}$ as follows,

  $\begin{array}{c}{a}_2=a_0+a_1\\ =1+3\\ =4\\ a_3=a_2+a_1\\ =4+3\\ =7\\ a_4=a_3+a_2\\ =7+4\\ =11\\ a_5=a_4+a_3\\ =11+7\\ =18\end{array}$

Hence the first five terms are

  $3,4,7,11,18$ .