Question

Interpole 12 meios aritméticos entre 3 e 42. calcule a soma dos termos e escreva a P.A

Answer 1

A PA terá um total de 14 termos...

Razão:

$a_1=3 \\ a_{14}=42 \\ r=\,?$

$a_n=a_1+(n-1)r \\ \\ 42=3+(14-1)r \\ \\ 42-3=13r \\ \\ 13r=39 \\ \\ \boxed{r=3}$

Soma:

$a_1=3 \\ a_{14}=42 \\ n=14 \\ \\ S_n= \frac{(a_1+a_n)n}{2} \\ \\ S_{14}= \frac{(3+42)\cdot14}{2} \\ \\ S_{14}=45\cdot7 \\ \\ S_{14}=315$

PA:

$(3;\,6;\,9;\,12;\,15;\,18;\,21;\,24;\,27;\,30;\,33;\,36;\,39;\,42)$