[tex] > resolucao \\ \\ \geqslant progressao \: geometrica \\ \\ a1 + a2 = 16 \\ a1 + a1q = 16 \\ a1(1 + q) = 16 \\ (1 + q) = \frac{16}{a1} \\ \\ \\ a3 + a4 = 144 \\ a1q {}^{2} + a1q {}^{3} = 144 \\ a1q {}^{2} (1 + q) = 144 \\ a1q {}^{2} ( \frac{16}{a1} ) = 144 \\ q {}^{2} = \frac{144}{16} \\ q {}^{2} = 9 \\ q = \sqrt{9} \\ q = +-3 \\ \\ \\ a1(1 + q) = 16 \\ a1(1 + 3) = 16 \\ 4a1 = 16 \\ a1 = \frac{16}{4} \\ a1 = 4 \\ \\ = = = = = = = = = = = = = = = = = = = = = = = \\ \\\\ \\ \\ \\ > \: o \: 7 \: termo \: da \: pg \\ \\ an = a1 \times q {}^{n - 1} \\ an = 4 \times 3 {}^{7 - 1} \\ an = 4 \times 3 {}^{6} \\ an = 4 \times 729 \\ an = 2916 \\ \\ \\ \\ > < > < > < > < > < > < > < > > [/tex]

a1 ( 1 + q ) = 16

a1 ( 1 - 3 ) = 16

- 2a1 = 16

a1 = - 16/2

a1 = - 8

7 termo da pg

an = a1 × q^n-1

an = - 8 × (-3)^7-1

an = - 8 × (-3)^6

an = - 8 × 729

an = - 5832

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