Question

Dany jest ciąg geom
3,6,12....
Podaj a10 i s12

Answer 1

A₁=3
q=6:3=2
a₁₀ = a₁ *q⁹
a₁₀ = 3*2⁹ = 3*512 = 1536
S₁₂=3*(1-2¹²)/(1-2) = 3*(2¹²-1)= 3*(4096-1)=12285

Answer 2

q = a2 / a1 = 6/3 = 2

q = 2

a1 = 3

an = a1 * q ^n-1

a10 = 3 * 2^9

Sn = a1 * (1 - q^n)/(1-q)

S12 = 3 * (1-2^12)/(1-2) = 3* [-(1-2^12) =  3* (-1 + 2^10) = -3 + 2^11