FIND WHICH TERM OF THE ARITHMETIC PROGRESSION WORKSHEET

Problem 1 :

1) For each question use the rule to find the first five terms of the sequence.

2) Can you find the 10^th term of the sequence ?

3) Can you find the 100^th term of the sequence ?

Rule :

2n - 1

Solution

Problem 2 :

Write the term to term rule for the sequence given below, then work out the next two terms.

4, 9, 14, 19, 24, .......

a) Is the number 37 in the sequence.

Solution

Problem 3 :

Calculate the difference between the 10^th term and 50^th term of the sequence

9, 14, 19, 24, ... ...

Solution

Problem 4 :

Find the n^th term for each of the following sequences

1/2, 3/4, 5/6, 7/8, .............

Solution

Problem 5 :

Write the next three terms of the arithmetic sequence.

a) First term: 2 Common difference: 13

b) First term: 18 Common difference: −6

Solution

Problem 6 :

write an equation for the nth term of the arithmetic sequence. Then find a₁₀.

−5, −4, −3, −2, . . ...

Solution

Problem 7 :

Describe and correct the error in finding the common difference of the arithmetic sequence.

Solution

Problem 8 :

Describe and correct the error in writing an equation for the nth term of the arithmetic sequence.

Solution

Problem 9 :

The first term of an arithmetic sequence is 3. The common difference of the sequence is 1.5 times the first term. Write the next three terms of the sequence. Then graph the sequence.

Solution

Write the first five terms of the sequence. Determine whether or not the sequence is arithmetic. If it is, find the common difference.

Problem 1 :

a_n = 8 +13n

Solution

Problem 2 :

a_n = (1/n) +1

Solution

Problem 3 :

a_n = 2ⁿ + n

Solution

Find the first four terms of the sequence given the explicit formula.

Problem 1 :

a_n = n² + 3

Solution

Problem 2 :

a_n = 15/(n + 3)

Solution

Problem 3 :

a_n = 2n - 1

Solution

Problem 4 :

a_n = n/(n +1)

Solution

Problem 5 :

a_n = 12 - 3n

Solution

Problem 6 :

a_n = 4n/3

Solution

Problem 7 :

In an auditorium, the first row of seats has 30 seats. Each row behind the first row has 4 more seats than the row in front of it. How many seats are in the 25th row?

Solution

Problem 8 :

Online bidding for a purse increases by $5 for each bid after the $60 initial bid.

a. Write a function that represents the arithmetic sequence.

b. Graph the function.

c. The winning bid is $105. How many bids were there?

Solution

Answer Key

1) first five terms of the sequence is 21, 34, 47, 60, 73.

the common difference (d) = 13

2) first five terms of the sequence is 2, 3/2, 4/3, 5/4, 6/5, d = -1/2

3) Since the common difference is not same, it is not arithmetic sequence.

1) first four terms of the sequence is 4, 7, 12, 17.

2)  first four terms of the sequence is 15/4, 3, 5/2, 15/7.

3)  first four terms of the sequence is 1, 3, 5, 7.

4) first four terms of the sequence is 1/2, 2/3, 3/4, 4/5.

5) first four terms of the sequence is 9, 6, 3, 0.

6) first four terms of the sequence is 4/3, 8/3, 4, 16/3.

7) 126

8) 

The function f(n) = 5n + 55 represents the arithmetic sequence.

b) Make a table. Then plot the ordered pairs (n, a_n).

There were 10 bids.

Find the n^th term of the arithmetic sequence.

Problem 1 :

a₁ = -4 and a₅ = 16

Solution

Problem 2 :

a₃ = 94 and a₆ = 85

Solution

Problem 3 :

a₅ = 190 and a₁₀ = 115

Solution

Problem 4 :

a₆ = -38 and a₁₁ = -73

Solution

Problem 5 :

a₃ = 19 and a₁₅ = -1.7

Solution

Problem 6 :

a₅ = 16 and a₁₄ = 38.5

Solution