Question

find the 14th term of the geometric sequence 3,6,12,24.

Answer 1

an=a1(r)^(n-1)
a1=first term
r=common rati

common ratio is a term divded by previous term
6/3=2
r=2

first term is 3

an=3(2)^(n-1)
14th term
a14=3(2)^(14-1)
a14=3(2)^13
a14=3(8192)
a14=24576

the 14th term is 24576

Answer 2

The Geometric Sequence can be defined as a sequence generated by multiplying by the same value each time.

The 14th term of the given geometric sequence is 24576.

How do you find out the 14th term of Geometric Sequence?

Given geometric sequence is 3, 6, 12, 24. There are 4 terms in the given sequence. The first term of the sequence is 3.

The general formula for the nth term of a geometric sequence is given below.

$a_n = a_1 \times r^{ (n-1)}$

Where a_1 is the first term of the sequence and r is the common ratio.

The common ratio for the given sequence is

$r = \dfrac {6}{3}$

$r = 2$

The 14th term of the given geometric sequence is given below.

$a_{14} = a_1\times r^{(14-1)}$

$a_{14} = a_1\times r^{13}$

$a_{14} = 3\times 2^{13}$

$a_{14} = 3\times 8192$

$a_{14} = 24576$

Hence, the 14th term of the given geometric sequence is 24576.

To know more about the geometric sequence, follow the link given below.

https://brainly.com/question/11266123.