The 7th term in the geometric sequence described by this explicit formula will be 31,250 so option (D) will be correct.
What is geometrical progression series?
A geometric progression is a sequence in which any element after the first is obtained by multiplying the previous element by a constant which is called a common ratio denoted by r.
For example, the sequence 1, 4, 16, 64,… is a geometric sequence with a common ratio of r = 4.
Given explicit formula is
[tex]a_{n}[/tex] = 2 × [tex]5^{(n-1)}[/tex]
Where n represents a number of terms and [tex]a_{n}[/tex] is an nth term in the GP series.
By substituting n = 7 into the formula
[tex]a_{7}[/tex] = 2 × [tex]5^{(7 - 1)}[/tex]
[tex]a_{7}[/tex] = 2 × 5⁶
[tex]a_{7}[/tex] = 2 × 15625 = 31250 hence, it will the correct answer.
For more information about the geometrical progression
brainly.com/question/4853032
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