Write a formula for the general term or nth term for the sequence. Then find the indicated term. \( -1,1,3,5,7, \ldots ; a_{12} \)

2) Intensidad de luz: un material traslúcido tiene la propiedad de reducir la intensidad de la luz que pasa a través de él. Un material traslucido de plástico tiene la propiedad de que una hoja de 1 mm de espesor reduce la intensidad de la luz en un \( 10 \% \). ¿Cuantas de tales hojas son necesarias para reducir la intensidad de un rayo de luz a cerca del \( 28 \% \) de su valor original?

Cabinet \( X \) costs \( \$ 30 \), requires 12 sq ft of floor space, and holds 36 cu ft of files. Cabinet \( Y \) costs \( \$ 50 \), requires 6 sq ft of floor space, and holds 30 cu ft . To get maximum storage, how many of each should be purchased with a budget limit of \( \$ 450 \) and floor space of 96 sq ft ? The manager should buy \( \square \) of cabinet \( X \) and \( \square \) of cabinet \( Y \). (If two possibilities provide maximum storage, use the option that involves buying at least one of cabinet \( X \) and at least one of cabinet \( ~ \) .)

Find the value of the determinant. \[ \left|\begin{array}{rrr}9 & 6 & 10 \\ -1 & -1 & 7 \\ -4 & -2 & 1\end{array}\right| \] The determinant value is

Aşağıdaki kutuların içine \( 2,4,6,8,70 \) ve 12 sayılarından dört tanesi her kutuya farkıı bir sayı gelecek şekilde yerleştirildiğinde eşitlik sağlanmaktadır. \[ \sqrt{\square}+\sqrt{\square}=\sqrt{\square+\square} \] Buna göre, kutulara yerleştirilmeyen sayılarín toplamı kaçtır? \( \begin{array}{llll}\text { (A) } 12 & \text { B) } 14 & \text { C) } 16 & \text { D) } 18\end{array} \) E) 20

3. Given the list of terms \( \frac{1}{3}, 1, \frac{5}{3}, \frac{7}{3}, \ldots \) a) Find the \( 15^{\text {th }} \) and \( -16^{\text {th }} \) term.