Find an explicit rule for the geometric sequence using subscript notation. Use a calculator and round your answers to the nearest tenth if necessary.The third term of the sequence is 170. The fifth term is 108.8.

Answer:The formula for nth term is given as [tex]a_n = (265.625)(0.8)^{(n-1)}[/tex]Step-by-step explanation:Here, 3rd term in the geometric sequence  =  170The 5th term in the sequence = 108.8Let the first term in the sequence = aLet the common ratio of the sequence = rNow by the Geometric Sequence:[tex]a_n = a(r^{n-1})[/tex]⇒ From above general term:  [tex]a_3  = a r^{2} ,\\ a_5 = ar^{4}[/tex]⇒[tex]170  = a r^{2} ,\\ 108.8 = ar^{4}[/tex]Dividing both the the equations, we get:[tex]\frac{170}{108.8}  = \frac{ar^2}{ar^4}  \implies 1.5625 = \frac{1}{r^2}[/tex]or, [tex]r^{2}   = \frac{1}{1.5625}  = 0.64\\ \implies r = 0.8[/tex]Hence, the common ratio r  = 0.8Now, [tex]170 =  a r^2  \implies 170 = a (0.64)\\\implies a = \frac{170}{0.64}  = 265.625[/tex]⇒ a =  265.625, r = 0.8So, the formula for nth term is given as [tex]a_n = (265.625)(0.8)^{(n-1)}[/tex]