Question

Find an equation for the nth term of a geometric sequence where the second and fifth terms are -2 and 16, respectively.

an = 1 • (-2)n - 1

an = 1 • 2n

an = 1 • (-2)n + 1

an = 1 • 2n - 1

Answer 1

\[a_n=a_1·r^{n-1}\rightarrow a_2=a_1·r / a_5=a_1·r^4\]\[\frac{ a_5 }{ a_2 }=r^3=\frac{ 16 }{-2 }=-8\rightarrow r=-2\]\[a_1=\frac{ a_2 }{ r }=\frac{ -2 }{ -2 }=1\]
\[a_n=\left( -2 \right)^{n-1}\]