Question

Dada a seguinte Progressão Geométrica(13,52,...,13631488),calcule:
a) q=
b) a9=
c) n=
d) Sn=

Answer 1

a) q = a₂ / a₁

q = 52/13

q = 4

b) a₉ = a₁ * q⁸

a₉ = 13 * 4⁸

a₉ = 13 * 65 536

a₉ = 8 519 68

c) An = a₁ * qⁿ⁻¹

13 631 488 = 13 * 4ⁿ⁻¹

4ⁿ⁻¹ = 13 631 488 / 13

4ⁿ⁻¹ = 1 048 576

4ⁿ⁻¹ = 4¹⁰

n - 1 = 10

n = 10 + 1

n = 11

d) Sn = a₁ * (qⁿ - 1) / q - 1

S₁₁ = 13 * (4¹¹ - 1) / 4 - 1

S₁₁ = 13 * (4 194 304 - 1) / 3

S₁₁ = 13 * (4 194 303) / 3

S₁₁ = 13 * 1 398 101

S₁₁ = 18 175 313

Answer 2

a) q= 4

b = a9= 13•4(8) = 52•8 = 416

c) 13631488 = 13•(4ⁿ⁺¹)

1048576 = 4ⁿ⁺¹

4¹⁰ = 4ⁿ⁺¹

n + 1 = 10

n = 9

d) Sn = a1 (qⁿ⁻¹)/q-1

Sn = 13 (4⁹-1)/4-1

Sn = 13( 262143)/3

Sn = 1135953

Sn =