Identify the correct form of the following geometric sequence.10 , 30 , 90 , 270 , …
To identify the correct form of a geometric sequence, we need to look for a common ratio between consecutive terms
To identify the correct form of a geometric sequence, we need to look for a common ratio between consecutive terms.
In this sequence, if we divide any term by the previous term, we will notice that the same ratio is obtained each time:
30/10 = 3
90/30 = 3
270/90 = 3
…
This common ratio is 3.
Therefore, the correct form of the geometric sequence is:
10 , 30 , 90 , 270 , …
We can represent this sequence using the formula:
a(n) = a(1) * r^(n-1)
where
a(n) represents the nth term of the sequence,
a(1) represents the first term of the sequence, and
r represents the common ratio.
In this case, since the first term is 10 and the common ratio is 3, the formula becomes:
a(n) = 10 * 3^(n-1)
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