Chapter 11.5, Problem 15PPS

To determine

The first five terms

Answer to Problem 15PPS

The first five terms are $-4,-7,-12,-21,-38$

Explanation of Solution

Given information:

  $a_1=-4,a_{n+1}=2a_n+n$

Concept used:

A recursive formula is used to express any term of the sequence in terms of the previous term, provided that the first term is given.

Calculation:

In order to find the first five terms as shown below

  $\begin{array}{c}{a}_1=-4\\ a_{n+1}=2a_n+n\\ a_2=2a_1+1=2\left(-4\right)+1\\ =-8+1\\ =-7\\ a_3=2a_2+2=2\left(-7\right)+2\\ =-14+2\\ =-12\\ a_4=2a_3+3=2\left(-12\right)+3\\ =-24+3\\ =-21\\ a_5=2a_4+4=2\left(-21\right)+4\\ =-42+4\\ =-38\end{array}$

Thus, the first five terms are $-4,-7,-12,-21,-38$