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.
[tex]$ n^{th} $[/tex] term of a Geometric progression is [tex]$ ar^{n - 1} $[/tex].
Note that the fourth term is 54.
i.e., [tex]$ ar^3 = 54 $[/tex]
[tex]$ \implies ar^4 = ar^3 . r = 54 . 3 = 162 $[/tex].
Similarly, [tex]$ ar^6 = 162 \times 3 = 486 $[/tex].
Also, [tex]$ ar^7 = ar^6 . r = 486 \times 3 = 1458 $[/tex].
Hence, OPTION B is the answer.
