Answer:
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Step-by-step explanation:
How To Find The nth Term Of A Geometric Sequence
Written by Hazmo in Geometric Sequence
The nth term is one of the most important element of geometric sequence.
It’s usually used to find out specific values within the geometric sequences.
We calculate the nth term by first finding the common ratio ‘r’ by dividing any two consecutive terms of the sequence.
And then we substitute ‘a‘ with the first term of the sequence and ‘n’ with the term number to get the final answer of the nth term.
The general formula to find the nth term is:
an=a1r(n–1)
Understanding the nth term of a geometric sequence gets easier if we know the meaning of this term and variables used.
Therefore, let’s first find what the nth term is and then move on to the details of it’s evaluation with different examples.
The rule that is generated is 3, 9, 27, ........ an.
"Geometric Progression (GP) is a type of sequence where each succeeding term is produced by multiplying each preceding term by a fixed number, which is called a common ratio. This progression is also known as a geometric sequence of numbers that follow a pattern."
Given,
a3 = 27
and r = 3
Formula for nth term is given by
[tex]a_{n} = a_{1}r^{n-1}[/tex]
so, we have
[tex]27 = a1.3^2[/tex]
so a1 = 3
Hence, the series becomes 3, 9, 27, ........an
To know more about geometric progression here
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