Question

Escreva os 5 primeiros termos das sequências definidas pelas leis de recorrência a seguir.
a) a1 = 1, an = an-1 -4, n£N e n>1
b) a1 = a2 = 1, an = an1 +an-2, n£N e n>2
c) a1 = 3, an= an-1 +1, n£N e n>1
                       10

Caso fique difícil de entender, abaixo tem um print da questão :

Answer 1

$a)\ a_1=1\ \ \ a_n = a_{n-1}-4\ \ \ n>1\\\\ Para\ n=2:\\ a_2=a_{2-1}-4\ \ \ \ a_2=a_1-4\ \ \ \ a_2=1-4\ \ \ \ a_2=-3\\\\ Para\ n=3:\\ a_3=-3-4\ \ \ \ a_3=-7\\\\ Para\ n=4:\\ a_4=-7-4\ \ \ \ a_4=-11\\\\ Para\ n=5:\\ a_5=-11-4\ \ \ \ a_5=-18\\\\\\ S=\{1, -3, -7, -11, -18\}$

$b)\ a_1=a_2=1\ \ \ \ \ a_n=a_{n-1}+a_{n-2}\ \ \ n>2\\\\ Para\ n=3:\\ a_3=a_{3-1}+a_{3-2}\ \ \ \ a_3=a_2+a_1\ \ \ \ a_3=1+1\ \ \ \ a_3=2\\ Para\ n=4:\\ a_4=a_{4-1}+a_{4-2}\ \ \ \ a_4=a_3+a_2\ \ \ \ a_4=2+1\ \ \ \ a_4=3\\ Para\ n=5:\\ a_5=a_{5-1}+a_{5-2}\ \ \ \ a_5=a_4+a_3\ \ \ \ a_5=3+2\ \ \ \ a_5=5\\ S=\{1, 1, 2, 3, 5\}$

$c)\ a_1=3\ \ \ \ a_n=\dfrac{a_{n-1}}{10}+1\ \ \ \ \ \ n>1\\\\ Para\ n=2:\\ a_2=\dfrac{3}{10}+1\ \ \ a_2=1,3\\\\\ Para\ n=3:\\ a_3=\dfrac{1,3}{10}+1\ \ \ a_3=1,13\\\\ Para\ n=4:\\ a_4=\dfrac{1,13}{10}+1\ \ \ a_4=1,113\\\\ Para\ n=5:\\ a_5=\dfrac{1,113}{10}+1\ \ \ a_5=1,1113\\\\\\ S=\{3,\ \ 1,3,\ \ 1,13,\ \ 1,113,\ \ 1,1113\}$

Bons estudos!