Chapter 3.6, Problem 9WE

To determine

Pattern and predict next two term of the sequence 2, 20, 10, 100, 50, …..

Answer to Problem 9WE

The next two terms of the sequence are $T_5=500\text{and }{T}_6=250$

Explanation of Solution

Given:

The given sequence is 2, 20, 10, 100, 50, …..

Let terms be

  $\begin{array}{l}{T}_0=2\\ T_1=20\\ T_2=10\\ T_3=100\\ T_4=50\end{array}$

Consider the alternate terms $T_0=2,T_2=10,T_4=50$

Here each next term is multiplied by 5.

So, the next term $T_6=50\times 5=250$

Now,

Consider the alternate terms $T_1=20,T_3=100$

Here also each next term is multiplied by 5.

So, the next term $T_5=100\times 5=500$

Therefore, the next two terms are $T_5=500\text{and }{T}_6=250$