Question

1)Determine a razão da PG
a) (3,12,48,...) b) (20,10, 5...) c) ( -8,16,-32,...) d) (5,5,5,...) e) (5,5/2,5/4...)

Answer 1

Explicação passo-a-passo:

olá,

a) (3,12,48,...)

an = a1 • q^(n-1)

a3 = 3 • q^(3-1)

48 = 3 • q²

48/3 = q²

16 = q²

√16 = q

√4² = q

4 = q

q = 4

—————

b) (20,10, 5...)

an = a1 • q^(n-1)

a3 = 20 • q^(3-1)

5 = 20 • q²

5/20 = q²

1/4 = q²

√1/4 = q

√1/√4 = q

√1/√2² = q

1/2 = q

q = 1/2

——————

c) ( -8,-16,-32,...)

an = a1 • q^(n-1)

a3 = -8 • q^(3-1)

-32 = -8 • q²

-32/-8 = q²

4 = q²

√4 = q

√2² = q

2 = q

q = 2

——————

d) (5,5,5,...)

an = a1 • q^(n-1)

a3 = 5 • q^(3-1)

5 = 5 • q²

5/5 = q²

1 = q²

√1 = q

1 = q

q = 1

——————

e) (5,5/2,5/4...)

an = a1 • q^(n-1)

a3 = 5/2 • q^(3-1)

5/4 = 5/2 • q²

5/4 / 5/2 = q²

5/4•2/5 = q²

10/20 = q²

1/2 = q²

√1/2 = q

√1/√2= q

(√1/√2)•(√2/√2) = q

(√2)/2 = q

q = (√2)/2 ou q = 0,7071

bons estudos!