1.Feladat
`a_n=a_1*q^(n-1)`

`a_4=a_1*q^(4-1)`

`48=6*q^3`

`8=q^3`

`color(red)(2=q)`


`a_n=a_1*q^(n-1)`

`a_3=a_1*q^(n-1)`

`a_3=6*2^2=color(red)(24)`


`S_n=a_1*(q^n-1)/(q-1)`

`S_10=6*(2^10-1)/(2-1)=color(red)(6.138)`



2.Feladat
`a_n=a_k+(n-k)*d`

`a_8=a_3+(n-k)*d`

`54=19+(8-3)*d`

`color(red)(d=7)`


`a_1=a_3-2d=19-2*7=color(red)(5)`


`S_n=((2*a_1+(n-1)*d)*n)/2`

`S_150=((2*5+(150-1)*7)*150)/2=color(red)(78.975)`



3.Feladat
`S_n=((2*a_1+(n-1)*d)*n)/2`

`S_7=((2*a_1+(n-1)*d)*n)/2`

`45,5=((2*2+(7-1)*d)*7)/2`

`45,5=14+21d`

`31,5=21`

`color(red)(1,5=d)`


`a_n=a_1+(n-1)*d`

`a_6=a_1+(n-1)*d`

`a_6=2+(6-1)*1,5=color(red)(9,5)`



4.Feladat
`S_n=((2*a_1+(n-1)*d)*n)/2`

`858=((2*8+(n-1)*2)*n)/2`

`858=7n+n^2`

`0=n^2+7n-858`


`n_(1,2) = (-b+-sqrt(b^2-4ac))/(2a)=(-7+-sqrt(7^2-4*1*(-858)))/(2)={(cancel(n_1=-33 )) , (color(red)(n_2 =26 )):}`

Tehát 26 sort rakott le.



5.Feladat
`364.985=200.000*(1+x)^10`

`(364.985)/(200.000)=1+x^10`

`root(10)((364.985)/(200.000))-1=x`

`color(red)(0,062=x)`

Tehát 6,2%-os kamaton helyeztük el a pénzünket.