Exploring Common Differences and Ratios in Real Life

A gardener plants a row of 5 trees. Each tree is planted 3 meters apart. If the first tree is at position 0, what is the position of the 5th tree? Calculate the common difference.

• 9 meters

• 12 meters

• 6 meters

• 15 meters

A car rental company charges a base fee of $20 and an additional $5 for each day the car is rented. If you rent the car for 7 days, how much will you pay in total? What is the common difference in the cost per day?

• Total cost: $50; Common difference: $4

• Total cost: $45; Common difference: $3

• Total cost: $60; Common difference: $6

• Total cost: $55; Common difference: $5

A student saves $10 in the first week and increases her savings by $5 each subsequent week. How much will she have saved by the end of 8 weeks? What is the common difference in her savings?

• Total savings: $180; Common difference: $10

• Total savings: $200; Common difference: $5

• Total savings: $220; Common difference: $5

• Total savings: $150; Common difference: $3

A book series has its first book priced at $15, and each subsequent book costs twice as much as the previous one. What is the price of the 4th book? Calculate the common ratio.

• $30

• $240

• $60

• $120

A factory produces 100 units in the first month and increases production by 20 units each month. How many units will be produced in the 6th month? What is the common difference?

• 200 units, common difference is 20 units

• 150 units, common difference is 30 units

• 180 units, common difference is 15 units

• 220 units, common difference is 25 units

A population of rabbits doubles every month. If there are 50 rabbits in the first month, how many will there be in the 4th month? Calculate the common ratio.

• 400

• 200

• 300

• 600

A concert hall has 200 seats in the first row, and each subsequent row has 10 more seats than the previous one. How many seats are in the 5th row? What is the common difference?

• 250 seats in the 5th row, common difference is 15.

• 240 seats in the 5th row, common difference is 10.

• 230 seats in the 5th row, common difference is 5.

• 200 seats in the 5th row, common difference is 20.

A savings account earns 2% interest compounded annually. If you start with $1,000, how much will you have after 3 years? Calculate the common ratio for the growth of your savings.

• $1,100.00

• $1,061.21

• $1,020.00

• $1,050.50

A movie theater sells 150 tickets on the first day, and ticket sales increase by 30 tickets each day. How many tickets will be sold on the 10th day? What is the common difference?

• 450 tickets, common difference is 40

• 390 tickets, common difference is 20

• 300 tickets, common difference is 30

• 420 tickets, common difference is 30

A sequence of numbers starts with 3 and each number is multiplied by 4 to get the next number. What is the 5th number in this sequence? Calculate the common ratio.

• 256

• 512

• 768

• 1024