Question

Numere $u_{1}, u_{2}, ..., u_{n}$ sunt in progresie geometrica. Sa se determine numarul acestora daca:
a) $u_{1}$ = 3, $u_{n}$ = 96, $S_{n}$ = 189
b) $u1_{1} , u_{n} = 2048$, $S_{n} = 189$

Answer 1

[tex]u_n=96=u_1*q^{n-1}=\ \textgreater \ 96=3q^{n-1}=\ \textgreater \ q^{n-1}=32\\ q^{n}=32q\\ S_n=u_1* \frac{q^n-1}{q-1} =\ \textgreater \ 189=3*\frac{32q-1}{q-1}=\ \textgreater \ \\ q=2=\ \textgreater \ 2^{n-1}=2^5=\ \textgreater \ n-1=5=\ \textgreater \ n=6\\
\[3,6,12,24,48,96\] [/tex]