Dada a progressão geométrica 1, 3, 9, 27, se a sua soma é 3280, quantos termos ela apresenta?
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Boa noite Giorgio!
Solução!
Basta substituir os dados na formula!
![Dados!\\\\\\
Sn=3280\\\\\\
a1=1\\\\\\\
q= \dfrac{a2}{a1}= \dfrac{3}{1}=3\\\\\\\
n=?](https://tex.z-dn.net/?f=Dados%21%5C%5C%5C%5C%5C%5C%0ASn%3D3280%5C%5C%5C%5C%5C%5C%0Aa1%3D1%5C%5C%5C%5C%5C%5C%5C%0Aq%3D+%5Cdfrac%7Ba2%7D%7Ba1%7D%3D+%5Cdfrac%7B3%7D%7B1%7D%3D3%5C%5C%5C%5C%5C%5C%5C%0An%3D%3F++ "Dados!\\\\\\
Sn=3280\\\\\\
a1=1\\\\\\\
q= \dfrac{a2}{a1}= \dfrac{3}{1}=3\\\\\\\
n=?")
![Formula!\\\\\\\
\boxed{Sn= \dfrac{a1(q^{n}-1) }{q-1}} \\\\\\\\\\\
3280= \dfrac{1(3^{n}-1) }{3-1} \\\\\\
3280= \dfrac{(3^{n}-1) }{2}\\\\\\
3280 \times2=3^{n}-1\\\\\\\
6560= 3^{n}-1\\\\\\\
6560+1= 3^{n}\\\\\\\
6561= 3^{n}\\\\\
Decompondo~~o ~~numero~~6561=3^{8} \\\\\\\
3^{8} =3^{n} \\\\\\
n=8](https://tex.z-dn.net/?f=Formula%21%5C%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7BSn%3D+%5Cdfrac%7Ba1%28q%5E%7Bn%7D-1%29+%7D%7Bq-1%7D%7D+%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%0A3280%3D+%5Cdfrac%7B1%283%5E%7Bn%7D-1%29+%7D%7B3-1%7D+%5C%5C%5C%5C%5C%5C%0A3280%3D+%5Cdfrac%7B%283%5E%7Bn%7D-1%29+%7D%7B2%7D%5C%5C%5C%5C%5C%5C%0A3280+%5Ctimes2%3D3%5E%7Bn%7D-1%5C%5C%5C%5C%5C%5C%5C%0A6560%3D+3%5E%7Bn%7D-1%5C%5C%5C%5C%5C%5C%5C%0A6560%2B1%3D+3%5E%7Bn%7D%5C%5C%5C%5C%5C%5C%5C%0A6561%3D+3%5E%7Bn%7D%5C%5C%5C%5C%5C%0ADecompondo%7E%7Eo+%7E%7Enumero%7E%7E6561%3D3%5E%7B8%7D+%5C%5C%5C%5C%5C%5C%5C%0A%0A3%5E%7B8%7D+%3D3%5E%7Bn%7D+%5C%5C%5C%5C%5C%5C%0An%3D8%0A%0A "Formula!\\\\\\\
\boxed{Sn= \dfrac{a1(q^{n}-1) }{q-1}} \\\\\\\\\\\
3280= \dfrac{1(3^{n}-1) }{3-1} \\\\\\
3280= \dfrac{(3^{n}-1) }{2}\\\\\\
3280 \times2=3^{n}-1\\\\\\\
6560= 3^{n}-1\\\\\\\
6560+1= 3^{n}\\\\\\\
6561= 3^{n}\\\\\
Decompondo~~o ~~numero~~6561=3^{8} \\\\\\\
3^{8} =3^{n} \\\\\\
n=8")
Boa noite!
Bons estudos!
Solução!
Basta substituir os dados na formula!
Boa noite!
Bons estudos!
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