Geometric Progression Solution

Problem Setup

We are asked to find the fifth term of a geometric progression (GP). We are given the first term ($a$) and the common ratio ($r$).

• First term ($a$): 2
• Common ratio ($r$): 3
• Term to find ($n$): 5

Geometric Progression Formula

The formula to calculate the $n$-th term ($a_n$) of a geometric progression is:

$a_n = a \cdot r^{(n-1)}$

Calculation Steps

Substitute the given values into the formula:

1. Identify the values: $a = 2$, $r = 3$, $n = 5$.
2. Apply the formula: $a_5 = a \cdot r^{(5-1)}$.
3. Simplify the exponent: $a_5 = 2 \cdot r^4$.
4. Substitute the common ratio: $a_5 = 2 \cdot 3^4$.
5. Calculate the power: $3^4 = 3 \times 3 \times 3 \times 3 = 81$.
6. Perform the final multiplication: $a_5 = 2 \times 81$.
7. Result: $a_5 = 162$.

Final Answer

The fifth term of the geometric progression is 162.