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Let n be the elements of the set B.
To determine the elements of the set, we'll have to solve the sum of the consecutive terms of a geometric progresison, that represents the property of the elements of the set.
The number of terms of the geometric progression is n+2. The common ratio of the geometric progression is q = 3.
The sum of n+2 terms of the geometric progression is:
S = b1*(q^(n+2) - 1)/(q-1)
Foe b1 = 1 and q = 3, we'll get:
S = [3^(n+2) - 1]/(3-1)
S = [3^(n+2) - 1]/2
But S = 1093 => [3^(n+2) - 1]/2 = 1093
Therefore, we'll have:
3^(n+2) - 1 = 2186
3^(n+2) = 2187
We'll create matching bases since 2187 = 3^7:
3^(n+2) = 3^7
Since the bases are matching, we'll apply one to one property:
n + 2 = 7
n = 5
The natural number that has the given property of the set B is n = 5.
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