Question

Find the 14th term of the geometric sequence 2, 6, 18,

Answer 1

Answer:

the 14 th term of the geometric sequence is = 3188646

Step-by-step explanation:

The geometric sequence is 2, 6, 18,...

The first term of the geometric sequence is =2

The common ratio of the given geometric sequence is = 6/2=18/6 = 3

Now we have to find the 14 th term of the given geometric sequence

Now we know , that is a is the first term of a geometric sequence , and r be the common ratio of the geometric sequence , then, the nth term of the geometric sequence is = a× r^(n-1)

So, here a = 2 and r = 3

So, the 14 th term of the geometric sequence is = 2×3^(14-1) = 2×3^13= 3188646

Answer 2

Given,

The geometric sequence is 2,6,18.

To find,

The 14th term of the geometric sequence.

Solution,

The first term of the sequence is 2.

The second term of the sequence is 6.

The third term of the sequence is 18.

In a geometric sequence, there is a constant ratio between the consecutive terms.

The geometric sequence looks like.

{a, a$r$, a$r^{2}$ a$r^{3}$, ... }

a=first term

r=ratio

Now in the sequence,

a(first term)=2

r = $\frac{ar}{a}$

r = $\frac{6}{2}$ = 3

Nth term of geometric sequence = $x_{n}$ = a$r^{n-1}$

$x_{14}$ = 2($3^{13}$) = 2(1594323 ) = 3188646

Hence, the 14th term of the geometric sequence 2,6,18 is 3188646.