7.2 Arithmetic sequences practice 1

Find the general forms of the following arithmetic sequences

(a) [math]a_{12}=a_3=7[/math]

(b) [math]a_4=d=2[/math]

Find the series of the following arithmetic sequences

(a) [math]a_7=10, a_1=-2[/math]. [math]S_{15}[/math]

(b) [math]a_{10}=30, a_6=18[/math]. [math]S_{50}[/math]

The summation of five consecutive even numbers is 600. Find these numbers. Write your answer in ascending order.

Let [math]\{a_n\}[/math] be an airthmetic sequence with [math]a_1=34[/math] and common difference [math]-3[/math]. Find the [math]n[/math] to maximize [math]S_n[/math].

(Calculator) Let [math]\{a_n\}[/math] be an arithmetic sequence with common difference [math]-3[/math]. If [math]a_1=399[/math] and [math]2^{a_1}\times2^{a_2}\times\cdots\times2^{a_n}<1[/math], what is the minimum of [math]n[/math]?

If [math]a_n[/math] is a sequence that satisfies [math]a_{10}=10[/math] and [math]a_{n+1}-a_n=-2[/math] for all [math]n\geq1[/math], which of the following statements is/are true?

If [math]a_n[/math] is a positive sequence that satisfies [math]a_1=12[/math] and the remainder of [math]a_k[/math] divided by 7 is always 5, which of the following statments is/are true?

Let [math]\{a_n\}[/math] be an arithmetic sequence with [math]a_1=34[/math] and [math]d=-3[/math]. Find the constant [math]n[/math] such that [math]S_n=-12[/math].

Ashley donates money to Happy temple every year. On the first year, she donated 250 dollars. On the second year, she donated 255 dollars. On the third year, she donated 260 dollars, and so on. Obeying this pattern, how much will she have donated after 20 years?

On 11/1, Eliza and Charlie conduct a debate in a lecture hall in Happy City. There are 15 rows of seats in the lecture hall. Let [math]\{a_n\}[/math] be a sequence representing the number of seats in the [math]n^{\text{th}}[/math] row. Suppose [math]a_3=19, a_{10}=40[/math]. How many seats are there in the lecture hall?