1,3,9,27,81,____What is the next number?
Answers
Answer:
243
Step-by-step explanation:
.………..….............. 1x3 , 3x3,9x3,27x3,81x3
81x3 = 243
Answer:
1. the next number = 243
2. the 12th number = 177147
Further explanation
Geometric sequences are a series of numbers that have a constant ratio
or can be interpreted:
Each number is obtained by multiplying the previous number by a constant
The sequence can be:
\tt a,ar,ar^2,ar^3...ar^{n-1}a,ar,ar
2
,ar
3
...ar
n−1
Can be formulated:
\tt a_n=ar^{n-1}a
n
=ar
n−1
where:
a is the first term, and
r is a common ratio
1, 3, 9, 27, 81, __
If we look at the series, then we can conclude that the series is a geometric sequence
So that the ratio value, r
\tt r=\dfrac{3}{1}=\dfrac{9}{3}=3r=
1
3
=
3
9
=3
the next number = a₆
\begin{gathered}\tt a_1=a=1\\\\r=3\\\\a_6=ar^{6-1}\\\\a_6=1.3^{5}\\\\a_6=243\end{gathered}
a
1
=a=1
r=3
a
6
=ar
6−1
a
6
=1.3
5
a
6
=243
the 12th number= a₁₂
\begin{gathered}\tt a_{12}=1.3^{12-1}\\\\a_{12}=3^{11}\\\\a_{12}=177147\end{gathered}
a
12
=1.3
12−1
a
12
=3
11
a
12
=177147
Learn more
the geometric sequence
https://brainly.ph/question/154960
Formula for geometric sequence
https://brainly.ph/question/2238923
Geometric sequence 1,5,25
https://brainly.ph/question/2261692
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