Question

Ciąg geometryczny

1.Oblicz a1 i n, jeśli:

q=1/2

an=5/16

Sn= 315/16

2. Oblicz 1n i n jeśli:

a1=4

q=3

Sn=13120

Answer 1

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

an=a1*q^(n-1)

a1=an/q^(n-1)

 

315/16=5/16*(1/2)^(1-n)(1-(1/2)^n)*2/:5/16

63=2((1/2)^(1-n)-1/2)

63=2*2^(n-1)-1

64=2^n

n=6

a1=5/16:(1/2)^5=5/16*32=10

Odp. a1=10, n=6

2.

13120=4*(1-3^n)/(1-3)

13120=-2+2*3^n

13122=2*3^n/:2

3^n=6561

3^n=81*81

3^n=3^(4+4)=3^8

n=8