Mathematics, 21.09.2019 20:00 math10030
Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -6 and 162, respectively. a. an = 2 • 3n - 1 b. an = 2 • (-3)n - 1 c. an = 2 • 3n d. an = 2 • (-3)n 1
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![a_2=-6\\a_5=162\\\\a_5:a_2=q^3\\\\q^3=162:(-6)\\q^3=-27\\q=\sqrt[3]{-27}\\q=-3\\\\a_n=a_1\cdot q^{n-1}\\\\a_1=a_2:q\to a_1=-6:(-3)=a_1=2\\\\\boxed{a_n=2\cdot(-3)^{n-1}\to b.}](/tpl/images/0250/1750/d13fa.png)
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