Chapter 7.10, Problem 15PPS

To determine

To find the first five terms of the given sequence.

Answer to Problem 15PPS

First five terms of the sequence are

  $\frac{1}{2},2,\frac{7}{2},5,\frac{13}{2}$ .

Explanation of Solution

Given:

  $a_1=\frac{1}{2},a_n=a_{n-1}+\frac{3}{2},n\ge 2$

Calculation:

  $\begin{array}{l}{a}_1=\frac{1}{2},a_n=a_{n-1}+\frac{3}{2},n\ge 2\\ \text{when}n=2,a_2=a_{2-1}+\frac{3}{2}\Rightarrow a_2=a_1+\frac{3}{2}\Rightarrow a_2=\frac{1}{2}+\frac{3}{2}\Rightarrow a_2=2\\ \text{when}n=3,a_3=a_{3-1}+\frac{3}{2}\Rightarrow a_3=a_2+\frac{3}{2}\Rightarrow a_3=2+\frac{3}{2}\Rightarrow a_3=\frac{7}{2}\\ \text{when}n=4,a_4=a_{4-1}+\frac{3}{2}\Rightarrow a_4=a_3+\frac{3}{2}\Rightarrow a_4=\frac{7}{2}+\frac{3}{2}\Rightarrow a_4=5\\ \text{when}n=5,a_5=a_{5-1}+\frac{3}{2}\Rightarrow a_5=a_4+\frac{3}{2}\Rightarrow a_5=5+\frac{3}{2}\Rightarrow a_5=\frac{13}{2}\end{array}$

Therefore first five terms of the sequence are $\frac{1}{2},2,\frac{7}{2},5,\frac{13}{2}$ .