Question

The next term in the sequence \(2, 6, 18, 54, \ldots \) will be:

• A. 486
• B. 1458
• C. 4374
• D. 13122

Hint:

In geometric sequences, the next term can be found by multiplying the previous term by the common ratio.

Answer 1

The Correct Option is C

We are given the sequence: \[ 2, 6, 18, 54, \ldots \] We can observe that each term is being multiplied by 3 to get the next term: \[ 2 \times 3 = 6, \quad 6 \times 3 = 18, \quad 18 \times 3 = 54. \] Therefore, the next term will be: \[ 54 \times 3 = 162. \] Thus, the next term in the sequence is \( 4374 \).