Question

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

152, 456, 1,368
162, 486, 1,458
172, 516, 1,548
182, 546, 1,638

Answer 1

OPTION B: 162, 486, 1458

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 * 3 = 486 $`.

Also,
`$ ar^7 = ar^6 . r = 486 * 3 = 1458 $`.

Hence, OPTION B is the answer.