The recursive rule for a geometric sequence is given a₁ = 6, aₓ = 1/4 aₓ₋₁. The explicit rule would be [tex]a_n = 6 (1/4)^{n-1}[/tex].
What is a geometric sequence and how to find its nth terms?
Suppose the initial term of a geometric sequence is a
and the term by which we multiply the previous term to get the next term is r
Then the sequence would look like
[tex]a, ar, ar^2, ar^3, \cdots[/tex]
Thus, the nth term of such sequence would be
[tex]T_n = ar^{n-1}[/tex]
We have been given the first term,
a₁ = 6.
The common ratio is the term aₓ divided by the previous term aₓ₋₁.
aₓ = 1/4 aₓ₋₁
aₓ / aₓ₋₁ = 1/4
r = 1/4
Therefore:
[tex]a_n = 6 (1/4)^{n-1}[/tex]
Hence, The explicit rule would be [tex]a_n = 6 (1/4)^{n-1}[/tex].
Learn more about geometric sequence here:
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