7.2 Arithmetic sequences (in class)

Consider a sequence [math]\{a_n\}=\sqrt{2}, \sqrt{8}, \sqrt{18}, \sqrt{32}, \sqrt{50}, \cdots[/math]. Which of the following values is between 1000 and 2000?

Let [math]\{a_n\}[/math] be an arithmetic sequence. Suppose [math]a_{12}=1[/math]. Find [math]S_{23}[/math]. (Hint: mid-term).

Let [math]\{a_n\}[/math] be an arithmetic sequence and [math]k[/math] be a nonzero constant. Which of the following sequences are also arithmetic?

Let [math]\{a_n\}[/math] be an arithmetic sequence. If [math]a_1+a_2+\cdots+a_n=\dfrac{-11n+31n^2}{2}[/math], what is the common difference?

Evaluate [math]-2+1+3+5+7+9+11+13+\cdots+199[/math]?

Given a sequence determined by [math]a_n=1-2n[/math], what is the summaion of the [math]501^{\text{st}}[/math] through the [math]1000^{\text{th}}[/math] terms of the sequence?

Insert 8 numbers between 1 and 12 to make the 10 numbers an arithmetic sequence. Find the common difference and the series.