Geometric sequence are sequence that increase exponentially. The explicit rule for the given sequence is Tn = [tex]729(0.67)^{n-1}[/tex]
Geometric sequence
Geometric sequence are sequence that increase expoenentially
The nth term of the sequence is expressed as [tex]Tn= ar^{n-1}[/tex]
If the fourth term of the sequence is 216, then;
[tex]T_4 = ar^3\\ar^3 = 216 .......... 1[/tex]
If the sixth tern is 96, then;
[tex]96 = ar^5\\ar^5 = 96 ........... 2[/tex]
Find the ratio
[tex]ar^5/ar^3 = 96/216\\r^2 = 96/216\\r = 0.67[/tex]
[tex]ar^3 =216\\a(0.67)^3 = 216\\0.296a = 216\\a = 729[/tex]
Hence the explicit rule for the given sequence is [tex]Tn =729(0.67)^{n-1[/tex]
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