91Ó°ÊÓ

Write the related series for each finite sequence. Then evaluate each series. $$ 21,18,15,12,9,6,3 $$

Evaluate the finite series for the specified number of terms. $$ 7-35+175-\ldots ; n=5 $$

Write a recursive formula for each sequence. Then find the next term. $$ 40,20,10,5, \frac{5}{2}, \dots $$

Find the 32nd term of each sequence. \(3,1,-1,-3, \dots\)

Use summation notation to write each arithmetic series for the specified number of terms. $$ (-3)+(-6)+(-9)+\ldots ; n=5 $$

Graph each curve. Use inscribed rectangles to approximate the area under the curve for the interval and rectangle width given. $$ y=x^{2}+1,1 \leq x \leq 3,0.5 $$

Graph each curve. Use inscribed rectangles to approximate the area under the curve for the interval and rectangle width given. $$ y=x^{2}+4,-2 \leq x \leq 2,0.5 $$

Architecture A 20 -row theater has three sections of seating. In each section, the number of seats in a row increases by one with each successive row. The first row of the middle section has 10 seats. The first row of each of the two side sections has 4 seats. a. Find the total number of chairs in each section. Then find the total seating capacity of the theater. b. Write an arithmetic series to represent each section. c. After every five rows, the ticket price goes down by \(\$ 5 .\) Front-row tickets cost \(\$ 60 .\) What is the total amount of money generated by a full house?

a. Open-Ended Write two explicit formulas for arithmetic sequences. b. Write the first five terms of each related series. c. Use summation notation to rewrite each series. d. Evaluate each series.

Approximate the area under the curve \(f(x)=x^{2}\) for the interval \(0 \leq x \leq 4\) by evaluating each sum. Use inscribed rectangles. a. \(\sum_{n=1}^{8}(0.5) f\left(a_{n}\right) \quad\) b. \(\sum_{n=1}^{4}(1) f\left(a_{n}\right)\) c. Which estimate is closer to the actual area under the curve? Explain.