7. Five marks example problems III

1. In a geometric progression, the \(4^{th}\) term is \(\frac{8}{9}\) and the \(7^{th}\) term is \(\frac{64}{243}\). Find the geometric progression.

 

Answer:

 

The geometric progression is $i,i,\frac{i}{i},...$

 

 

2. The product of three consecutive terms of a geometric progression is \(343\) and their sum is  \(\frac{91}{3}\). Find the three terms.

 

Answer:

 

When $r=i$:

 

The three terms are $\frac{i}{i},i,i$.

 

 

 

3. The present value of a machine is \(₹40,000\) and its value depreciates each year by \(10\%\). Find the estimated value of the machine in the \(6^{th}\) year.

 

Answer:

 

The estimated value of the machine in the \(6^{th}\) year \(=\) \(₹\)$i$

 

[Note: Round off your answer to one decimal place.]