Question

Em uma PG,o primeiro termo é raiz de 2, eo terceiro termo é raiz 14 de 2 elevado a 9. Calcule o décimo termo.?

Answer 1

a3 = a1 r^2 

2^(9/14) = raiz(2) • r^2 = 2^(1/2) • r^2 

r^2 = 2^(9/14)/2^(1/2) = 2^(9/14-1/2) =2^(2/14) = 2^(1/7) 

Logo r = 2^(1/14) 

O termo 10 é: 

a10 = a1•r^(n-1) = 2^(1/2) • (2^(1/14))^9 = 2^(1/2) • 2^(9/14) = 2^(16/14) = 2^(8/7)

Answer 2

$a_3=a_1\cdot q^2\\\\\sqrt[14]{2^9}=\sqrt{2}\cdot q^2\\\\2^{\frac{9}{14}}=2^{\frac12}\cdot q^2\\\\q^2=\frac{2^{\frac{9}{14}}}{2^{\frac12}}\\\\q^2=2^{\frac{9}{14}-\frac12}\\\\q^2=2^{\frac{2}{14}}\\\\q=\sqrt{2^{\frac{2}{14}}}\\\\q=2^{\frac{1}{14}}\\\\a_{10}=a_1\cdot q^9\\\\a_{10}=2^{\frac12}\cdot (2^{\frac{1}{14}})^9\\\\a_{10}=2^{\frac12}\cdot2^{\frac{9}{14}}\\\\a_{10}=2^{\frac{8}{7}}=\sqrt[7]{2^8}$