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# Sequences: Word Problems

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## Sequences: Word Problems Answer Key

1.
A cargo train has 120 cars. The first car is carrying 3 small boxes, the second car is carrying 5 small boxes, the third car is carrying 7 small boxes, and so on. How many small boxes are in the 98th train car?
1. 194
2. 199
3. 196
4. 197
2.
Sarah is training for a marathon. Each day, she runs a little bit longer than the last. If she runs 2 miles the first day, 4 miles the second day, 6 miles the third day, and so on, how many miles does she run on the 15th day?
1. 29
2. 30
3. 31
4. 32
3.
Kai is trying to write a book and plans on writing at least 3.5 more pages each day than he did the last. If he wrote 7 pages yesterday, how many pages will he write in 10 days?
1. 73.5
2. 45.5
3. 42
4. 38.5
4.
Carol started biking to work each day. Ever since she started, she has been getting in better shape, and notices that her daily trip is decreasing slightly. If her trip took 58 and a half minutes three days ago, 57 minutes and 15 seconds two days ago, and 56 minutes yesterday, about how long will her trip take her in 5 days from today, assuming this pattern continues?
1. 46 minutes
2. 48 minutes and 30 seconds
3. 52 minutes and 15 seconds
4. 53 minutes and 30 seconds
5.
Sam is trying to reduce the amount of money he spends on coffee each month. He currently spends about $300 per month on coffee. The average price for each coffee he buys is around$4. For the current month, Sam will continue buying as many coffees as he usually does. Next month he plans on buying 3 fewer coffees than he currently buys, then 3 fewer the month after that, and then 3 fewer the next month, and so on till he is spending less than $20 per month on coffee. If Sam sticks to his plan, about how much will he be spending on coffee in 7 months? 1.$216
2. $228 3.$204
4. $236 6. A ball rolling down an incline travels 2 meters in the first second, 4 meters the second, and 8 meters the third second. How far will it roll in the 10th second? 1. 256 meters 2. 2,046 meters 3. 20 meters 4. 1,024 meters 7. A small petri dish currently contains 12 bacteria cells. If the bacteria double every hour, how many bacteria cells will there be in 24 hours? 1. 50,331,648 2. 100,663,296 3. 201,326,592 4. 402,653,184 8. Simon has a savings account, and each year he checks the balance. When he was 20, the balance was$1,000. When he was 21, the balance was $1,010. When he was 22, the balance was$1,020.10. If his account continues to grow at the same rate, how much will it have when he is 30 years old?
1. $1104.62 2.$1093.69
3. $1100.00 4.$1110.00
9.
A certain substance exhibits radioactive decay. 18 hours after the initial amount was left out, there is 12 grams of the substance remaining. 18 hours later there is 10.2 grams remaining, and then 8.67 grams 18 hours after that. About how much of the substance is left after 12 days and 18 hours since the starting amount?
1. 1.23 g
2. 1.05 g
3. 0.89 g
4. 0.64 g
10.
A new spaceship has been developed. It has many small rocket thrusters that can be used together. If just one thruster is used, the ship travels at a speed of 3,000 miles per hour. Each additional thruster causes the ship to travel 15% faster. However, each thruster uses 500 gallons of fuel per hour. About how fast is the spaceship traveling if it is using 4,500 gallons of fuel per hour? Round answers to the nearest mile per hour.
1. 12,137 mph
2. 7,980 mph
3. 10,554 mph
4. 9,177 mph
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