Odpowiedź:
[tex]\huge\boxed{C. \ 5}[/tex]
Jeśli (aₙ) jest ciągiem arytmetycznym o różnicy r, to
[tex]a_{n} = a_1 +(n-1)\cdot r[/tex]
dla dowolnego n ∈ N₊
[tex]a_5 = 7 \ \ oraz \ \ a_7 = 11\\a_{4} = ?[/tex]
[tex]a_1 + 4r = 7\\a_1 + 6r = 11\\\\a_1 + 4r - a_1 - 6r = 7-11\\\\-2r = -4 \ \ \ /:(-2)\\\\\underline{r = 2}\\\\a_1 + 4r = 7\\\\a_1 + 4\cdot2 = 7\\\\a_1 + 8 = 7 \ \ \ |-8\\\\\underline{a_1 = -1}\\\\\\a_4 = a_1 + 3r\\\\a_4 = -1 + 3\cdot 2\\\\a_4 = -1+6\\\\\boxed{a_4 = 5}[/tex]
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Verified answer
Odpowiedź:
[tex]\huge\boxed{C. \ 5}[/tex]
Ciąg arytmetyczny
Jeśli (aₙ) jest ciągiem arytmetycznym o różnicy r, to
[tex]a_{n} = a_1 +(n-1)\cdot r[/tex]
dla dowolnego n ∈ N₊
[tex]a_5 = 7 \ \ oraz \ \ a_7 = 11\\a_{4} = ?[/tex]
[tex]a_1 + 4r = 7\\a_1 + 6r = 11\\\\a_1 + 4r - a_1 - 6r = 7-11\\\\-2r = -4 \ \ \ /:(-2)\\\\\underline{r = 2}\\\\a_1 + 4r = 7\\\\a_1 + 4\cdot2 = 7\\\\a_1 + 8 = 7 \ \ \ |-8\\\\\underline{a_1 = -1}\\\\\\a_4 = a_1 + 3r\\\\a_4 = -1 + 3\cdot 2\\\\a_4 = -1+6\\\\\boxed{a_4 = 5}[/tex]