Question

insira 7 meios aritmético entre 25 e 7​

Answer 1

Interpolando 7 meios aritméticos, estaremos formando uma PA com 9 termos sendo que a₁=25 e a₉=7.

                             {25 , a₂ , a₃ , a₄ , a₅ , a₆ , a₇ , a₈ , 7}

Vamos então começar determinando a razão r dessa PA com auxilio da equação do termo geral da PA:

$a_n~=~a_1~+~(n-1)\cdot r\\\\\\a_9~=~a_1~+~(9-1)\cdot r\\\\\\7~=~25~+~8r\\\\\\8r~=~7-25\\\\\\r~=~\dfrac{-18}{8}\\\\\\r~=\,-\dfrac{9}{4}\\\\\\\boxed{r~=\,-2,25}$

Podemos agora determinar os termos que foram interpolados utilizando, novamente, a equação do termo geral:

$a_2~=~a_1+r~=~25-2,25~~~\rightarrow~~~\boxed{a_2~=~22,75}\\\\\\a_3~=~a_2+r~=~22,75-2,25~~~\rightarrow~~~\boxed{a_3~=~20,50}\\\\\\a_4~=~a_3+r~=~20,50-2,25~~~\rightarrow~~~\boxed{a_4~=~18,25}\\\\\\a_5~=~a_4+r~=~18,25-2,25~~~\rightarrow~~~\boxed{a_5~=~16}\\\\\\a_6~=~a_5+r~=~16-2,25~~~\rightarrow~~~\boxed{a_6~=~13,75}\\\\\\a_7~=~a_6+r~=~13,75-2,25~~~\rightarrow~~~\boxed{a_7~=~11,50}\\\\\\a_8~=~a_7+r~=~11,50-2,25~~~\rightarrow~~~\boxed{a_8~=~9,25}$

A PA fica: {25 ; 22,75 ; 20,50 ; 18,25 ; 16 ; 13,75 ; 11,50 ; 9,25 ; 7}