Răspuns:
420
Explicație pas cu pas:
[tex]a_{4} - a_{2} = 4 \\ a_{1} + 3\cdot r - a_{1} - r = 4 \\ 2\cdot r = 4 \implies \bf r = 2[/tex]
[tex]a_{1} + a_{3} + a_{5} + a_{6} = 30[/tex]
[tex]a_{1} + a_{1} + 2 \cdot r + a_{1} + 4 \cdot r + a_{1} + 5 \cdot r = 30 \\ [/tex]
[tex]4 \cdot a_{1} + 11 \cdot 2 = 30 \iff 4 \cdot a_{1} = 30 - 22 \\ a_{1} = 8 : 2 \implies \bf a_{1} = 2[/tex]
[tex]a_{20} = a_{1} + 19 \cdot r = 2 + 19 \cdot 2 = 2 + 38 = 40 \\ [/tex]
[tex]S_{n} = \frac{(a_{1} + a_{n})\cdot n}{2} \\ [/tex]
[tex]S_{20} = \frac{(2 + 40)\cdot 20}{2} = \bf 420 \\ [/tex]
