Arithmetic Sequences Problem Solving

After knee surgery, your trainer tells you to return to your jogging program slowly. He suggests jogging for 12 minutes each day for the first week. Each week thereafter, he suggests that you increase that time by 6 minutes per day.

What are the first term and the common difference?

• the first term 6 and common difference 12

• the first term 12 and common difference 6

• the first term 6 and common difference -6

• the first term 12 and common difference 12

After knee surgery, your trainer tells you to return to your jogging program slowly. He suggests jogging for 12 minutes each day for the first week. Each week thereafter, he suggests that you increase that time by 6 minutes per day.

How long would you be running each day in week 3?

• 24 minutes

• 30 minutes

• 20 minutes

• 36 minutes

After knee surgery, your trainer tells you to return to your jogging program slowly. He suggests jogging for 12 minutes each day for the first week. Each week thereafter, he suggests that you increase that time by 6 minutes per day.

How many weeks will it be before you are up to jogging 60 minutes per day?

• 7 weeks

• 8 weeks

• 9 weeks

• 10 weeks

A theater has 60 seats in the first row, 68 seats in the second row, 76 seats in the third row, and so on in the same increasing pattern.

What are the first term and the common difference?

• a₁=60, d=68

• a₁=60, d=8

• a₁=60, d= -8

• a₁=8, d=60

A theater has 60 seats in the first row, 68 seats in the second row, 76 seats in the third row, and so on in the same increasing pattern.

If the theater has 20 rows of seats, how many seats are in the 20th row of the theater?

• 172 seats

• 180 seats

• 188 seats

• 212 seats

A display of cans on a grocery shelf consists of 20 cans on the bottom, 18 cans in the next row, and so on in an arithmetic sequence, until the top row has 4 cans.

What are the first term and the common difference?

• a₁₌20 d=2

• a₁₌ 20 d= -2

• a₁₌ -20 d= 18

• a₁₌ 20 d= - 18

A display of cans on a grocery shelf consists of 20 cans on the bottom, 18 cans in the next row, and so on in an arithmetic sequence, until the top row has 4 cans.

How many rows are there on the display?

• 7 rows

• 8 rows

• 9 rows

• 10 rows

A pile of bricks has 97 bricks in the first row, 91 bricks in the second row, 85 bricks in the third row, and so on until there is only one brick in the top row.

What explicit formula is used to calculate number of bricks in the nth row?

• a_n=97+91(n-1)

• a_n=97-91(n-1)

• a_n=97 - 6(n-1)

• a_n=97 + 6(n-1)

A pile of bricks has 97 bricks in the first row, 91 bricks in the second row, 85 bricks in the third row, and so on until there is only one brick in the top row.

How many bricks are in the 15th row?

• 0 bricks

• 1 brick

• 7 bricks

• 13 bricks

Amara has to stack her neighbor's wood. She starts by putting 15 logs in the bottom row (row 1), 13 logs in the second row (row 2), 11 in the third row (row 3) and continues in the same pattern. She can only stack as high as her head, at 8 rows. How many logs are in the 8th row?

• 0 logs

• 1 log

• 29 logs

• 31 logs