How do you find the nth term rule for #-3,12,-48,192,...#?

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Answer 1 · 2016-08-26T13:36:57

#t_n=3/4(-4)^n#.

Let us denote, by #t_n#, the #n^(th)# term of the seq.

We find that, #t_2/t_1=-4, t_3/t_2=-4, t_4/t_3=-4,...#

We conclude that the given seq. is a Geometric Seq., with,

#t_1=-3, "&, common ratio r=-4"#

The Formula for the General Term #t_n# for a Geo. Seq. is,

#t_n=t_1*r^(n-1)=-3*(-4)^(n-1)=3/4(-4)^n#.

Enjoy Maths.!