Asynchronous ActivityProblems Involving SequencesDirection: Write the letter of your answer in your notebook.1. A cinema has 15 seats in the first row, 16 on the 2nd row, 17 on the 3rd row. If the pattern continues up tothe 8th row, how many seats are in the cinema?A. 172B. 164C. 156D. 1482. A bus tour company has 7 different buses. If the first bus can accommodate 40 passengers, the second buscan accommodate 45 passengers, the third bus can accommodate 50 passengers and so on, what is the totalnumber of passengers in all 7 buses?A. 265B. 385C. 435D. 5453. A car travels 40 km after 1 hour, 90 km after 2 hours, and 140 km after 3 hours. If it continues to travel atthis rate, how many kilometers will it travel after 10 hours?A. 490B. 510C. 630D. 7504. A stack of soap boxes must be patiently arranged by Samantha. If there must be 12 boxes in the bottomrow, 11 boxes in the second bottom row, 10 in the next and so on until the topmost row has 1 box. How manyboxes are in the stack?A. 64B. 78C. 86D. 925. A car travels 180m the first minute, 250m the next minute, 320m the third minute and so on. How manyminutes does the car traveled after 5 minutes?B. 340mC. 280mD. 120mA. 460m6. A student saved 10 pesos on Sunday and doubled his savings each day thereafter. What was his totalearnings for the week?A. 1270B. 930C. 850D. 6407. To find the sum of infinite geometric sequence, what formula is the best to use?A. S₁ = (a + an)B. STL =C. S=(1-)D. S1-ra1-an1-r8. Which of the following is the result of adding the terms of geometric sequence with a common ration of-1 A. Finite Geometric SequenceB. Infinite Geometric SequenceC. Finite Geometric SeriesD. Infinite Geometric Series9. A pendulum that is released to swing freely travels 18 inches on the first swing. On each successive swing,the pendulum travels 80% of the distance of the previous swing. This problem is an example of what kind ofsequence? what will be the total distance of the pendulum until it stops?A. 90 inB. 18 inC. 80 inD. 8 in10. A ball tossed to a height of 4 meters rebounds to 30% of its previous height. Find the total distance bythe ball by the time it comes to rest.A. 11.43 mB. 13.33 mC. 14 mD. 18 m
Answer (1)
Answer:Here are the answers to the problems: 1. C. 156 - This is an arithmetic sequence with a common difference of 1. To find the total number of seats, we need to find the sum of the first 8 terms. The formula for the sum of an arithmetic sequence is Sn = (n/2)(a1 + an), where Sn is the sum of the first n terms, a1 is the first term, and an is the nth term.- In this case, n = 8, a1 = 15, and a8 = 15 + (8-1)1 = 22.- Therefore, S8 = (8/2)(15 + 22) = 156.2. D. 545 - This is an arithmetic sequence with a common difference of 5. To find the total number of passengers, we need to find the sum of the first 7 terms.- Using the same formula as above, n = 7, a1 = 40, and a7 = 40 + (7-1)5 = 60.- Therefore, S7 = (7/2)(40 + 60) = 545.3. C. 630 - This is an arithmetic sequence with a common difference of 50. To find the total distance traveled after 10 hours, we need to find the sum of the first 10 terms.- Using the same formula, n = 10, a1 = 40, and a10 = 40 + (10-1)50 = 490.- Therefore, S10 = (10/2)(40 + 490) = 630.4. B. 78 - This is an arithmetic sequence with a common difference of -1. To find the total number of boxes, we need to find the sum of the first 12 terms.- Using the same formula, n = 12, a1 = 12, and a12 = 12 + (12-1)(-1) = 1.- Therefore, S12 = (12/2)(12 + 1) = 78.5. A. 460m - This is an arithmetic sequence with a common difference of 70. To find the total distance traveled after 5 minutes, we need to find the sum of the first 5 terms.- Using the same formula, n = 5, a1 = 180, and a5 = 180 + (5-1)70 = 460.- Therefore, S5 = (5/2)(180 + 460) = 460.6. D. 640 - This is a geometric sequence with a common ratio of 2. To find the total earnings for the week, we need to find the sum of the first 7 terms.- The formula for the sum of a geometric sequence is Sn = a1(1-r^n)/(1-r), where Sn is the sum of the first n terms, a1 is the first term, and r is the common ratio.- In this case, n = 7, a1 = 10, and r = 2.- Therefore, S7 = 10(1-2^7)/(1-2) = 640.7. C. S= a1/(1-r) - This is the formula for the sum of an infinite geometric sequence, where a1 is the first term and r is the common ratio. This formula only works if the absolute value of the common ratio is less than 1 (|r| < 1).8. D. Infinite Geometric Series - A geometric series is the sum of the terms in a geometric sequence. When the common ratio is -1, the terms alternate between positive and negative values, resulting in an infinite geometric series.9. A. 90 in - This is an example of a geometric sequence with a common ratio of 0.8. To find the total distance the pendulum travels until it stops, we need to find the sum of an infinite geometric sequence.- Using the formula from question 7, a1 = 18 and r = 0.8.- Therefore, S = 18/(1-0.8) = 90.10. B. 13.33 m - This is an example of an infinite geometric sequence with a common ratio of 0.3. To find the total distance the ball travels, we need to consider both the upward and downward distances.- The upward distances form a geometric sequence: 4, 1.2, 0.36, ...- The downward distances form the same geometric sequence, except for the initial 4 meters.- Therefore, the total distance is: 4 + 2 * (4/(1-0.3)) = 13.33 meters.
