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\begin{document}

\begin{center}
\textbf{Progresii}
\end{center}

1. Fie progresia aritmetica $a_1,a_2,\dots,a_n,\dots\quad\ ,n\in\textbf{N}$
$$
\begin{array}{ll}
d=a_n-a_{n-1};              & a_n=a_1+d(n-1);\\
\ds S_n=\frac{a_1+a_n}{2}n; & \ds S_n=\frac{2a_1+d(n-1)}{2}
\end{array}
$$
unde $d$ - ratia progresiei, $a_n$ - termenul de rang $n$,
$S_n$ - suma primilor $n$ termeni ai progresiei.\\

2. Fie progresia geometrica $b_1,b_2,\dots,b_n,\dots\quad\ ,n\in\textbf{N}$

$$
\begin{array}{ll}
  \ds q=\frac{b_n}{b_{n-1}};\\[5mm]
  \ds b_n=b_1q^{n-1};\\[2mm]
  \ds S_n=\frac{a_nq-a_1}{q-1} &
      \ds\left(S_n=\frac{a_1-a_nq}{1-q}\right);\\[5mm]
  \ds S_n=\frac{a_1(q^n-1)}{q-1} &
      \ds\left(S_n=\frac{a_1(1-q)^n}{1-q}\right)
\end{array}
$$
unde $q$ - ratia progresiei, $S_n$ - suma primilor $n$ termeni ai
progresiei.\\

Suma progresiei geometrice infinit descrescatoare este
$$
S=\frac{b_1}{1-q}
$$
unde $|q|<1$.

\footnotetext[0]{\quad Copyright$\copyright$1999 ONG TCV
    Scoala Virtuala a Tanarului Matematician \quad http://math.ournet.md}

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