Question

Expresse pelo termo geral cada sequência dada abaixo:
a) (1,10,2,10²,3,10³,...)
b) (1,9,25,49,81,...)
c) (1/2,-1/4,1/6,-1/8,1/10,...)
d) (0,3/2,-2/3,5/4,-4/5,7/6,...)
gente da uma força.

Answer 1

a)

$(1,10,2,10^2,3,10^3,...)$

$\boxed{\boxed{\begin{Bmatrix}se~n=par,~a_n=10^{\frac{n}{2}}\\\\se~n=impar,~a_n=\frac{n+1}{2}\end{matrix}}}$

b)

$(1,9,25,49,81,...)$

$\boxed{\boxed{a_n=(2n-1)^2}}$

c)

$\left(\frac{1}{2},-\frac{1}{4},\frac{1}{6},-\frac{1}{8},\frac{1}{10},...\right)$

$\boxed{\boxed{a_n=\frac{1}{2n}*(-1)^{(n-1)}}}$

d)

$\left(0,\frac{3}{2},-\frac{2}{3},\frac{5}{4},-\frac{4}{5},\frac{7}{6},...\right)$

$\boxed{\boxed{\begin{Bmatrix}se~n=par,~a_n=1+\frac{1}{n}\\\\se~n=impar,~a_n=\frac{-n+1}{n}\end{matrix}}}$