Explicație pas cu pas:
c) progresie aritmetică
[tex]a_{1} = 2, r = 3, n = 10[/tex]
[tex]S_{n} = \frac{(a_{1} + a_{n}) \cdot n}{2} \\ [/tex]
[tex]| + 2| + | + 5| + | + 8| + ... + | + 29| = \\ [/tex]
[tex]= 2 + 5 + 8 + ... + 29 \\ [/tex]
[tex]= 2 + (2 + 1 \cdot 3) + (2 + 2 \cdot 3) + ... + (2 + 9\cdot 3) \\[/tex]
[tex] = \frac{(2 + 29) \cdot 10}{2} = \frac{31\cdot 10}{2} = 155 \\ [/tex]
d) progresie geometrică
[tex]b_{1} = 2, q = 2, n = 20 [/tex]
[tex]S_{n} = \frac{b_{1} \cdot ({q}^{n} - 1)}{q - 1} \\ [/tex]
[tex]{ | - 2| }^{1} + { | - 2| }^{2} + { | - 2| }^{3} + ... + { | - 2| }^{20} = \\ [/tex]
[tex]= {2}^{1} + {2}^{2} + {2}^{3} + ... + {2}^{20} \\ [/tex]
[tex]= \frac{2 \cdot ( {2}^{20} - 1)}{2 - 1} \\ [/tex]
[tex]= 2 \cdot ( {2}^{20} - 1) \\ [/tex]
