Question

Interpole oito meios aritméticos entre os números -2 e 43.

Answer 1

Vejamos:
an = 43
a1 = -2
n = 10
r = ?

43 = -2 + 9r
9r = 43 + 2
9r = 45
r = 45/9
r = 5
Daí teremos: PA = ( -2,3,8,13,18,23,28,33,38,43)
meios aritméticos: 3,8,13,23,28,33,38

Answer 2

$\textsf{Descobrindo a raz\~ao:}\\\\\\\mathsf{q=\dfrac{b-a}{K+1}}\\\\\\\mathsf{Onde~b=43,~a=-2~~e~~K=meios~a~seres~interpolados.}\\\\\\\mathsf{q=\dfrac{43-(-2)}{8+1}}\\\\\\\mathsf{q=\dfrac{43+2}{9}}\\\\\\\mathsf{q=\dfrac{45}{9}}\\\\\\\mathsf{q=5}$


$\textsf{F\'ormula de recorr\^encia:}\\\\\mathsf{a_1+q=a_2}\\\\\mathsf{a_2+q=a_3}\\\\.\\.\\.\\\\\mathsf{a_n+q=a_{a_n+1}}\\\\\\\textsf{Logo, os 8 \underline{meios} interpolados em P.A ser\~ao:}\\\\\\(-2\hspace{-7}\diagup,\underline{3,8,13,18,23,28,33,38},43\hspace{-8}\diagup)\\\\\\\rightarrow\mathsf{(3,8,13,18,23,28,33,38)}~~~~\Large\checkmark$