5. What is an annuity? Algebraic For the following exercises, express each description of a sum using summation notation, . ESUIT'I CI _ _ _1 E. The sum that results from adding the number 4 five times For the following exercises. express each arithmetic sum using summation notation. W 131I1|3l2| Id For the following exercises. use the formula for the sum of the first :2 terms of each arithmetic sequence. 3 5 1 E. i + 2 + E + 3 + E dds-MM For the following exercises. express each geometric sum using summation notation. W .3+4+2+...+.125 For the following exercises+ use the formula for the sum of the first rt terms of each geometric sequence. and than state the indicated sum. 1] a. Z 64 - 0.2"' a=l For the following exercises, determine whether the infinite series has a sum. If so, write the formula tor the sum. If not, state the reason. m ml m=l =1 kl a2- H Graphical For the following exercises, use the following scenario. Javier makes monthly deposits into a savings account. He opened the account with an initial deposit of 550. Each month thereafter he increased the previous deposit amount by $20. 26. Blaptl HIE millllelic 3\"\"! ICE Slll'liilg W + I . 3. Graph the arithmetic series showing the monthly sums of one year of Javier's deposits. k m 1 For the following exercises, use the geometric series 2 (E) . i=1 a. What number does 3,, seem to be approaching in the graph? Find the sum to explain why this makes sense. Numeric For the following exercises, nd the indicated sum. For the following exercises, use the formula for the sum of the first :1 terms of an arithmetic series to find the sum. EEG-3 For the following exercises use the formula for the sum of the first in terms of a geometric series to find the partial sum. 45. 4.6 . 0.50-1 1=1 For the following exercises, determine the value of the annuity for the indicated monthly deposit amount, the number of deposits, and the interest rate. 46. Deposit amount. $50, total deposits. 60, interest rate. 59%, compounded monthly- 47. Deposit amount: $150, total deposits: 24; interest rate: 3%%, compounded monthly- 48. Deposit amount. $450, total deposits. 60, interest rate. 4.59%, compounded quarterly- 49. Deposit amount: $100; total deposits: 120; interest rate: 10%, compounded semi-annually Extensions 60. The sum of terms 50 / from / x through 7 is 115. What is *? ST. Write an explicit formula for ax such that Z Uk - 109. Assume this is an arithmetic series. K= 0 52 Find the smallest value of A such that ) (3*-5) - 100. k=1 53. How many terms must be added before the series -1 - 3 - 5 - 7.... has a sum less than -75?57. Karl has two years to save $10, 000 to buy a used car when he graduates. To the nearest dollar, what would his monthly deposits need to be if he invests in an account offering a 4.2% annual interest rate that compounds monthly? Real-World Applications 56. Keisha devised a week long study plan to prepare for finals. On the first day, she plans to study for 1 hour, and each successive day she will increase her study time by 30 minutes. How many hours will Keisha have- studied after one week?- 59. A boulder rolled down a mountain, traveling 0 feet in the first seeend. Each suseeseive second, its distance increased by 0 feet. How far did the boulder travel after 10 seeends? 60. A celentist places 60 oelle in a petri dish. Every hour, the population increases by 1.6%. What will the sell count be after 1 day2 61. A pendulum travels a distance of 3 feet on its first swing. On each successive swing, it travels , the distance of the previous swing. What is the total distance traveled by the pendulum when it stops swinging