Question

find the 9th term of 2,6,18,54-----

Answer 1

5th term is
$54 \times 3 = 162$
6th term is
$162 \times 3 = 486$
7th term is
$486 \times 3 = 1458$
8th term is
$1458 \times 3 = 4374$
9th term is
$4374 \times 3 = 13122$

Answer 2

Given sequence is 2,16,18,54...

It is in GP because 2 * 3 = 6, 6 * 3 = 18, 18 * 3 = 54...There is a common ratio between each term.

We know that nth term of a geometric sequence an = ar^n-1.  ---------- (1)

In this equation a1 = 2, r = 3.   ----------- (2)

Substitute (2) in (1), we get

a9 = (2) * (3)^n - 1

a9 = (2) * (3)^9 - 1(Since we are finding the 9th term, n value should be 9).

a9 = (2) * (3)^8

a9 = 2 * 6561

a9 = 13122.


Therefore the 9th term in the sequence is 13122.

Hope this helps!