Question

What are the next three terms in the pattern 2, 6, 18, 54, ...?

Answer 1

Answer:

OPTION B: 162, 486, 1458

Step-by-step explanation:

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

It is a geometric sequence and the common difference is 3.

The general form of a geometric sequence is: a, ar, ar², ar³, . . .

Here a = 2 and r = 3.

$n^{th}$ term of a Geometric progression is $ar^{n - 1}$.

Note that the fourth term is 54.

i.e., $ar^3 = 54$

$\implies ar^4 = ar^3 . r = 54 . 3 = 162$.

Similarly, $ar^6 = 162 \times 3 = 486$.

Also, $ar^7 = ar^6 . r = 486 \times 3 = 1458$.

Hence, OPTION B is the answer.

Answer 2

Answer:

B

Step-by-step explanation: