Question

Se considera progresia geometrica( bn)n mai mare si egal ca 1 in care b1=4,b4=10.Calculati b25

Answer 1

Formula termenului general a unei progresii geometrice:

$b_n=b_1\cdot q^{n-1}$
Unde q este ratia.

[tex]b_4=b_1\cdot q^3=10\\ 4\cdot q^3=10\\ q= \sqrt[3]{\frac{5}{2}} [/tex]
$b_{25}=b_1\cdot q^{24}=4\cdot (\sqrt[3]{\frac{5}{2}})^{24}=4\cdot (\frac{5}{2})^8= \frac{5^8}{2^6}$