Geometric Progression
1. What is the sum of the geometric sequence 8, –16, 32 … if there are 15 terms? (1 point) = 8 [(-2)^15 -1] / [(-2)-1] = 87384
2. What is the sum of the geometric sequence 4, 12, 36 … if there are 9 terms? (1 point) = 4(3^9 - 1)/(3 - 1) = 39364
3. What is the sum of a 6-term geometric sequence if the first term is 11, the last term is –11,264 and the common ratio is –4? (1 point) = -11 (1-(-4^n))/(1-(-4)) = 11(1-(-11264/11))/(1-(-4)) = 2255
4. What is the sum of an 8-term geometric sequence if the first term is 10 and the last term is
781,250? (1 point) =8 (1-390625)/(1-5) =781,248
For problems 5 8, determine whether the problem should be solved using the formula for an arithmetic sequence, arithmetic series, geometric sequence, or geometric series. Explain your answer in complete sentences. You do not need to solve.
5. Jackie deposited $5 into a checking account in February. For each month following, the deposit amount was doubled. How much money was deposited in the checking account in the month of August? (1 point) To solve this, a geometric sequence is used because the terms share a constant ratio as 2.
6. A local grocery store stacks the soup cans in such a way that each row has 2 fewer cans than the row below it. If there are 32 cans on the bottom row, how many total cans are on the bottom 14 rows? (1 point) To solve you use a formula for an arithmetic series because for every row, the number of cans keep decreasing.
7. A major US city reports a 12% increase in decoration sales during the yearly holiday season. If decoration sales were 8 million in 1998, how much did the city report in total decoration sales by the end of 2004?(1 point) You would use a geometric series formula because the increase will be different each year because the percentage increase affects the outcome of the next years by a common ratio.
8. A fireplace contains 46 bricks along its bottom row. If each row above decreases by
2. What is the sum of the geometric sequence 4, 12, 36 … if there are 9 terms? (1 point) = 4(3^9 - 1)/(3 - 1) = 39364
3. What is the sum of a 6-term geometric sequence if the first term is 11, the last term is –11,264 and the common ratio is –4? (1 point) = -11 (1-(-4^n))/(1-(-4)) = 11(1-(-11264/11))/(1-(-4)) = 2255
4. What is the sum of an 8-term geometric sequence if the first term is 10 and the last term is
781,250? (1 point) =8 (1-390625)/(1-5) =781,248
For problems 5 8, determine whether the problem should be solved using the formula for an arithmetic sequence, arithmetic series, geometric sequence, or geometric series. Explain your answer in complete sentences. You do not need to solve.
5. Jackie deposited $5 into a checking account in February. For each month following, the deposit amount was doubled. How much money was deposited in the checking account in the month of August? (1 point) To solve this, a geometric sequence is used because the terms share a constant ratio as 2.
6. A local grocery store stacks the soup cans in such a way that each row has 2 fewer cans than the row below it. If there are 32 cans on the bottom row, how many total cans are on the bottom 14 rows? (1 point) To solve you use a formula for an arithmetic series because for every row, the number of cans keep decreasing.
7. A major US city reports a 12% increase in decoration sales during the yearly holiday season. If decoration sales were 8 million in 1998, how much did the city report in total decoration sales by the end of 2004?(1 point) You would use a geometric series formula because the increase will be different each year because the percentage increase affects the outcome of the next years by a common ratio.
8. A fireplace contains 46 bricks along its bottom row. If each row above decreases by