Question

Interpole sete meios aritméticos entre -25 e 118.​

Answer 1

Interpolar meios aritméticos é inserir números entre outros dois de modo que a sequência seja uma progressão aritmética.

$\mathsf{P.A~(-25,\underline{a_{2} },\underline{a_{3}}\underline,\underline{a_{4} },\underline{a_{5} },\underline{a_{6} },\underline{a_{7}},\underline{a_{8}},118)}$

$\mathsf{a_{1}=-25}\\\mathsf{a_{9}=118}$

$\mathsf{a_{9}=a_{1}+8r}\\\mathsf{118=-25+8r}$

$\mathsf{8r=118+25}\\\mathsf{8r=143}\\\mathsf{r=\dfrac{143}{8}}$

$(-25,\underline{-\dfrac{57}{8}},\underline{\dfrac{43}{4}},\underline{\dfrac{229}{8}},\underline{\dfrac{93}{2}},\underline{\dfrac{515}{8}},\underline{\dfrac{329}{4}},\underline{\dfrac{801}{8}},118)$