Question

Faça a interpolção de 
a)7 meios entre 7 e -9
b)9 meios entre 11 e 1
c)8 meios entre 5 e 50
d)6 meios entre a e 15a

Answer 1

$A)\\ a1=7\\ an=-9\\ n=9\\ \\ an=a1+(n-1)r\\ -9=7+(9-1)r\\ -9=7+9r-r\\ -9-7=8r\\ -16=8r\\ \frac { -16 }{ 8 } =r\\ -2=r\\ \\ P.A\quad \{ 7,5,3,1,-1,-3,-5,-7,-9\}$

$B)\\ a1=11\\ an=1\\ n=11\\ \\ an=a1+(n-1)r\\ 1=11+(11-1)r\\ 1-11=11r-r\\ -10=10r\\ \frac { -10 }{ 10 } =r\\ -1=r\\ \\ P.A=\quad \{ 11,10,9,8,7,6,5,4,3,2,1\}$

$C)\\ a1=5\\ an=50\\ n=10\\ \\ an=a1+(n-1)r\\ 50=5+(10-1)r\\ 50-5=10r-r\\ 45=9r\\ \frac { 45 }{ 9 } =r\\ 5=r\\ \\ P.A=\quad \{ 5,10,15,20,25,30,35,40,45\}$

$D)\\ a1=a\\ an=15a\\ n=8\\ \\ an=a1+(n-1)r\\ 15a=a+(8-1)r\\ 15-a=8r-r\\ 14a=7r\\ \frac { 14a }{ 7 } =r\\ 2a=r\\ \\ P.A=\quad \{ a,3a,5a,7a,9a,11a,13a,15a\}$