Question

1. (FEI - SP) A sequˆencia (a1, a2, . . . , an) ´e definida por:
a1 = 1/5
a2 = 0
an = an−1 + an−2, n ≥ 3

Qual o valor de a7?

a) 1/5 b) 2/5 c) 3/5 d) 4/5 e) 1

Answer 1

Boa noite!!

Se: $a_{n} = a_{n-1} + a_{n-2}$ , devemos substituir os valor até achar a7.

$a_{3} = a_{3-1} + a_{3-2}$
$a_{3} = a_{2} + a_{1}$
$a_{3} = 0 + \frac{1}{5}$
$a_{3} = \frac{1}{5}$

$a_{4} = a_{4-1} + a_{4-2}$
$a_{4} = a_{3} + a_{2}$
$a_{4} = \frac{1}{5} + 0$
$a_{4} = \frac{1}{5}$

$a_{5} = a_{5-1} + a_{5-2}$
$a_{5} = a_{4} + a_{3}$
$a_{5} = \frac{1}{5} + \frac{1}{5}$
$a_{5} = \frac{2}{5}$

$a_{6} = a_{6-1} + a_{6-2}$
$a_{6} = a_{5} + a_{4}$
$a_{6} = \frac{2}{5} + \frac{1}{5}$
$a_{6} = \frac{3}{5}$

$a_{7} = a_{7-1} + a_{7-2}$
$a_{7} = a_{6} + a_{5}$
$a_{7} = \frac{3}{5} + \frac{2}{5}$
$a_{7} = \frac{5}{5}$

Assim:
$a_{7} = 1$
Letra E