[tex] - 5, - 1,3,7,11,15.[/tex]
Termenii şirului sunt în progresie aritmetică :
[tex]a_{1} = - 5[/tex]
[tex]a_{2} = - 1[/tex]
[tex]a_{2} = a_{1} + r[/tex]
[tex]r = a_{2} - a_{1} [/tex]
[tex]r = a_{2} - a_{1}[/tex]
[tex]r = - 1 - ( - 5)[/tex]
[tex]r = - 1 + 5[/tex]
[tex]r = 4[/tex]
[tex]a)a_{n} = a_{1} +r (n - 1)[/tex]
[tex]a_{12} = - 5 + 4(12 - 1)[/tex]
[tex]a_{12} = - 5 + 4 \times 11[/tex]
[tex]a_{12} = - 5 + 44[/tex]
[tex]a_{12} = 39[/tex]
[tex]b)S_{n} = \frac{n(a_{1} + a_{n})}{2}[/tex]
[tex]S_{12} = \frac{12( - 5 + 39)}{2} [/tex]
[tex]S_{12} = \frac{12 \times 34}{2} [/tex]
[tex]S_{12} = 6 \times 34[/tex]
[tex]S_{12} = 204[/tex]
[tex]c)a_{48} = - 5 + 4(48 - 1)[/tex]
[tex]a_{48} = - 5 + 4 \times 47[/tex]
[tex]a_{48} = - 5 + 188[/tex]
[tex]a_{48} = 183[/tex]
[tex]d)S_{48} = \frac{48( - 5 + 183)}{2} [/tex]
[tex]S_{48} = \frac{48 \times 178}{2} [/tex]
[tex]S_{48} = 24 \times 178[/tex]
[tex]S_{48} = 4272[/tex]
