Question

Dada a PG (9, 3, 1, . . . , 1/81 ), calcule a) a razão; b) o número de termos.

Answer 1

an=1/81
a1=9
q=1/3
n=?

a) a2/a1=3/9= 1/3

b) an=a1.q⁽ⁿ⁻¹⁾
    1/81=9.1/3⁽ⁿ⁻¹⁾
    1/81/9=1/3⁽ⁿ⁻¹⁾
    1/729=1/3⁽ⁿ⁻¹⁾
    729⁻¹=(3⁻¹)⁽ⁿ⁻¹⁾
    729⁻¹=3⁻ⁿ⁺¹
    (3⁶)⁻¹=3⁻ⁿ⁺¹
    3⁻⁶=3⁻ⁿ+1 Corta as bases
    -6=-n+1
    n=1+6
    n=7

Answer 2

resolução!

q = a2 / a1

q = 3 / 9

q = 1 / 3

an = a1 * q^n - 1

1/81 = 9 * (1/3)^n - 1

1/81 ÷ 9 = (1/3)^n - 1

1/81 * 1/9 = (1/3)^n - 1

1/729 = (1/3)^n - 1

( 1/3)^6 = ( 1/3 )^n - 1

n - 1 = 6

n = 6 + 1

n = 7 termos