Morgan Newton
02/28/2024 · Middle School

8. Zadan je aritmetički niz \( \left(a_{n}\right) \). Izračunajte prvi član, razliku i opći član niza. \( \begin{array}{ll}\text { a) } a_{2}+a_{5}=23, a_{4}+a_{10}=44 & \text { b) } a_{7}+a_{15}=0, a_{13}-a_{6}=\frac{7}{2} \\ \text { c) } a_{11}-a_{6}=-2, a_{17}+a_{17}=-10 & \text { d) } a_{2}+a_{7}=60, a_{3} \cdot a_{7}=704\end{array} \)

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a) Prvi član: \( a_1 = 4 \), razlika: \( d = 3 \), opći član: \( a_n = 3n + 1 \) b) Prvi član: \( a_1 = -5 \), razlika: \( d = \frac{1}{2} \), opći član: \( a_n = \frac{n-1}{2} - 5 \) c) Prvi član: \( a_1 = \frac{3}{5} \), razlika: \( d = -\frac{2}{5} \), opći član: \( a_n = \frac{5 - 2n}{5} \) d) Prvi član i razlika mogu se izračunati iz jednadžbi, opći član se određuje na isti način.

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