Question

2. Resolva

a) Determine o 15º termo da PG (256, 128, 64, ...)

b) Calcule a soma dos 8 primeiros termos da PG (4, 8, 16 ... 1024).

c) calcule a soma dos primeiros seis termos da P.G. (1,3,9)​

Answer 1

a)

$q = \frac{a2}{a1} = \frac{128}{256} = 1/2$

$an = a1.q^{n-1}\\\\a15 = a1.(1/2)^{14}\\\\a15 = 256/2^{14}\\\\a15 = 2^{8}/2^{8}.2^{6}\\\\a15 = 1/2^{6}\\\\a15 = 1/64$

b)

$S = \frac{a1(q^{n}-1)}{q-1}$

$S = \frac{4(2^{8}-1)}{2-1}\\\\S = {4(2^{8}-1)$

$S = {2^{2}.2^{8}-2^{2}$

$S = {2^{10} - 4 = 1020$

c)

$S = \frac{a1(q^{n}-1)}{q-1}\\\\S = \frac{1(3^{6}-1)}{3-1}\\\\S = \frac{(3^{6}-1)}{2}\\\\S = \frac{728}{2}\\\\S = 364$