Respuesta :
To find the explicit formula of geometric sequences, you'll need to find a formula for the nth term.
In symbols, the nth term of a geometric sequence is: tn = a·rn-1.
a = first term and r = common ratio
To find the common ratio, divide any term by its preceding term.
Example: 2, 6, 18, 54, 162, ...
a = first term = 2
r = common ratio = 6/3 = 2 (this will be the same anywhere you begin: 162/54 = 3, 54/18 = 3, 18/6 = 3, etc.)
So, the explicit formula is: tn = 2·3n-1
Each explicit formula will have the exponent "n-1".
The answer to your question would be; tn = 2·3n-1.
Hope this helped.
The explicit rule to find the nth term of the sequence that is given will be an = 2 × 3n - 1.
The geometric sequence that is given is 2, 6, 18, 54, … It can be deduced that the first term is 2. The common ratio will be: = 6/2 = 3.
Therefore, since we know the first term and the common ratio, the nth term of the sequence will be;
= a × rn - 1
= 2 × 3n - 1
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