Question

Interpole 5 meios aritmeticos entre -5 e 37

Answer 1

5   __  __  __ __  __ 37
(1) (2) (3) (4) (5) (6) (7)
$a_{7} = a_{1} +6r \\ 37 = 5+6r \\ 32=6r \\ r= \frac{16}{3}$
$a_{n} =a_{n-1} + r \\ a_{2} =5 + \frac{16}{3} = \frac{31}{3} \\ a_{3} = \frac{31}{3} + \frac{16}{3} = \frac{47}{3} \\ a_{4} = \frac{47}{3} + \frac{16}{3} = \frac{63}{3} = 21 \\ a_{5} =21 + \frac{16}{3} = \frac{79}{3} \\ a_{6} = \frac{79}{3} + \frac{16}{3} = \frac{95}{3}$
R = $(\frac{31}{3}, \frac{47}{3}, 21, \frac{79}{3}, \frac{95}{3})$