The 8^th term of the sequence 2, 6, 18, 54, ________ is

Given:

The sequence is: 2, 6, 18, 54, ...

We need to find the 8^th term of the sequence.

Formula used:

The given sequence is a Geometric Progression (GP).

The nth term of a GP is given by: \(a_n = a \times r^{(n-1)}\)

Where:

• a = First term of the sequence
• r = Common ratio
• n = Position of the term to be found

Calculation:

Here, a = 2

To find r, divide the second term by the first term:

r = 6 ÷ 2 = 3

We need to find the 8^th term:

\(a_8 = a \times r^{(8-1)}\)

\(a_8 = 2 \times 3^7\)

Calculate 3⁷:

3⁷ = 3 × 3 × 3 × 3 × 3 × 3 × 3 = 2187

Substitute the value of 3⁷:

⇒ \(a_8 = 2 \times 2187\) = 4374

∴ The correct answer is option (2).