Arithmetic Sequence and Series

Basic

1

What is the formula in determining the n^th term of an Arithmetic Sequence

a_n=a₁+(n-1)d

2

What is the common difference in 3, 11, 19, 27, 35, ...? What is the 6th term?

d=8, 6th term=43

3

Find the next term in the sequence 7,15,23,31, __.

39

4

Find the first five terms of the sequence a_n=10-2n

a₁=10-2(1) =8; a₂=10-2(2) =6; a₃=10-2(3) =4; a₄=10-2(4) =2; a₅=10-2(5) =0

5

Determine the second term of the following arithmetic sequence:      2,  ____ , 26 

14

Word Problems

1

You visit the Grand Canyon and drop a penny off the edge of a cliff. The distance the penny will fall is 16 feet the first second, 48 feet the next second, 80 feet the third second, and so on in an arithmetic sequence. What is the total distance the object will fall in 6 seconds?

576 feet

2

Which term of the arithmetic sequence

3, 15, 27, 39, ... is 132 more than its 54th term? 

65

3

How many three-digit numbers are divisible by 7?

128

4

How many multiples of 4 lie between 10 and 250?

60

5

A hardware store makes a profit of 30,000 pesos during its first year. The store owner sets a goal of increasing profits by 5,000 pesos each year for 4 years. Assuming that this goal is met, find the total profit during the first 5 years of business

200,000 pesos

Not So Difficult

1

Which term of the arithmetic sequence 3,8,13,18,... is 78?

16

2

Find the 20th term from the last term of the AP: 

3, 8, 13, ..., 253

158

3

Find the common difference of the arithmetic sequence with a₄=10 and a₁₁= 45.

5

4

How many terms are there in an arithmetic sequence with a common difference of 4 and with first and last terms 3 and 59, respectively?

15

5

What must be the value of k so that 5k – 3, k + 2, and 3k – 11 will form an arithmetic sequence?

3

Challenge

1

A water tank develops a leak. Each week, the tank loses 5 gallons of water due to the leak. Initially, the tank is full and contains 1500 gallons. How many weeks until the tank is empty?

The tank is empty after 300 weeks.

2

For what value of n, are the nth terms of two arithmetic progressions 63, 65, 67,... and 3, 10, 17,... equal?

13

3

Determine the AP whose third term is 16 and the 7th term exceeds the 5th term by 12.

4, 10, 16, ...

4

Two arithmetic sequences have the same common difference. The difference between their 100th term is 100, What is the difference between their 1000th terms?

100

5

The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.

- 13, -8, -3