Question

dados
a1=81
an=16
n=5
hallar
r=?
sn=?

Answer 1

an = a1*[r^(n-1)]

a1 = 81; a5 = 16; n = 5

16 = 81*[r^(5-1)]

16 = 81*[r^4]

r^4 = 16/81

16 = 2^4

81 = 3^4

r^4 = (2^4/3^4)

$r =\sqrt[4]{ \frac{2^{4}}{3^{4}}} =2/3$

r = 2/3


Sn = [(an*r - a1)/(r - 1)]

Sn = S5

S5 = [(16*(2/3) - 81)/((2/3) - 1)]

S5 = [(32/3 - 81)/(-1/3)]

S5 = [(-211/3)/(-1/3)] = 211

S5 = 211

Rta: r = 2/3; S5 = 211