Question

13. Na P.G. (3, 6, 12, ...) calcule: a) o décimo termo;​

Answer 1

$> resolucao \\ \\ \geqslant progressao \: \: geometrica \\ \\ a1 = 3 \\ a2 = 6\\ n = 10 \\ \\ q = \frac{a2}{a1} \\ q = \frac{6}{3} \\ q = 2 \\ \\ \\ > \: o \: decimo \: termo \: da \: pg \\ \\ \\ an = a1 \times q {}^{n - 1} \\ an = 3 \times 2 {}^{10 - 1} \\ an = 3 \times 2 {}^{9} \\ an = 3 \times 512 \\ an = 1536 \\ \\ \\ \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \geqslant$

Answer 2

$a10 = 1536$

Para calcular o décimo termo da PG, aplica-se a fórmula $an = a1.q^{(n - 1)}$

$q = a2 / a1\\\\q = 6 / 3\\\\q = 2$

$an = a1.q^{(n - 1)}\\ \\a10 = 3.2^{(10 - 1)}\\ \\a10 = 3.2^9\\\\a10 = 3.512\\\\a10 = 1536$

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