Determine o número de termos da pa (4,9,14,...,84)
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Bom dia !
Solução!
![P.A\{4,9,14........84\}\\\\\\
a1=4\\\\
r=a2-a1=9-4=5\\\\\
an=84\\\\\
n=?\\\\\\\\\\
Formula!\\\\\\
an=a1+(n-1).r\\\\\\\
84=4+(n-1).5\\\\\\
84=4+5n-5\\\\\\
84=-1+5n\\\\\\
84+1=5n\\\\\
85=5n\\\\\\
5n=85\\\\\\
n= \dfrac{85}{5}\\\\\
n=17\\\\\\
Resposta: A~~P.A~~tem~~17~~termos.](https://tex.z-dn.net/?f=P.A%5C%7B4%2C9%2C14........84%5C%7D%5C%5C%5C%5C%5C%5C%0Aa1%3D4%5C%5C%5C%5C%0Ar%3Da2-a1%3D9-4%3D5%5C%5C%5C%5C%5C%0Aan%3D84%5C%5C%5C%5C%5C%0An%3D%3F%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%0AFormula%21%5C%5C%5C%5C%5C%5C%0Aan%3Da1%2B%28n-1%29.r%5C%5C%5C%5C%5C%5C%5C%0A84%3D4%2B%28n-1%29.5%5C%5C%5C%5C%5C%5C%0A84%3D4%2B5n-5%5C%5C%5C%5C%5C%5C%0A84%3D-1%2B5n%5C%5C%5C%5C%5C%5C%0A84%2B1%3D5n%5C%5C%5C%5C%5C%0A85%3D5n%5C%5C%5C%5C%5C%5C%0A5n%3D85%5C%5C%5C%5C%5C%5C%0An%3D+%5Cdfrac%7B85%7D%7B5%7D%5C%5C%5C%5C%5C%0An%3D17%5C%5C%5C%5C%5C%5C%0AResposta%3A+A%7E%7EP.A%7E%7Etem%7E%7E17%7E%7Etermos.+%0A "P.A\{4,9,14........84\}\\\\\\
a1=4\\\\
r=a2-a1=9-4=5\\\\\
an=84\\\\\
n=?\\\\\\\\\\
Formula!\\\\\\
an=a1+(n-1).r\\\\\\\
84=4+(n-1).5\\\\\\
84=4+5n-5\\\\\\
84=-1+5n\\\\\\
84+1=5n\\\\\
85=5n\\\\\\
5n=85\\\\\\
n= \dfrac{85}{5}\\\\\
n=17\\\\\\
Resposta: A~~P.A~~tem~~17~~termos.")
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Bons estudos!
Solução!
Bom dia!
Bons estudos!
Respondido por
1
an= a1 + (n-1).r
84=4 + (n-1).5
84-4= 5n-5
80+5=5n∴85=5n∴ n=85/5=17
84=4 + (n-1).5
84-4= 5n-5
80+5=5n∴85=5n∴ n=85/5=17
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