Question

Dada a PG

(2, 6, 18... 39366)

Determine:
a) O termo Geral
b) O número de termos
c) A soma dos termos

Answer 1

$a_n=39366 \\ a_1=2 \\ r=q=6\div2=3 \\ \\ termo~~geral \\ \\ a_n=a_1.q^{n-1} \\ \\ 39366=2.3^{n-1} \\ \\ 39366\div2=3^{n-1} \\ \\ 19683=3^{n-1} \\ \\\not 3^{n-1}=\not3^9 \\ \\ n-1=9 \\ n=9+1 \\ n=10~~termos \\ \\ Soma \\ \\ S_n= \frac{a_1(q^n-1)}{q-1} \\ \\ S_{10}= \frac{2(3^{10}-1)}{3-1} \\ \\ S_{10}= \frac{\not2(59049-1)}{\not2} ] \\ \\ S_{10}=59048$