# Worksheet: Finding the Arithmetic Sequence

In this worksheet, we will practice finding arithmetic sequences given some information about it.

Q1:

Find the arithmetic sequence in which and .

• A
• B
• C
• D

Q2:

Find the arithmetic sequence given , and all terms are positive.

• A
• B
• C
• D

Q3:

Find the arithmetic sequence whose ninth term is , and the arithmetic mean between the third and fifth terms is .

• A
• B
• C
• D
• E

Q4:

Find the arithmetic sequence for which and is the additive inverse of .

• A
• B
• C
• D
• E

Q5:

Find an arithmetic sequence given and .

• A
• B
• C
• D
• E

Q6:

Find the arithmetic sequence in which the sum of the first and third terms equals , and the sum of its third and fourth terms equals .

• A
• B
• C
• D

Q7:

The first and last terms of an arithmetic sequence are and 209 respectively. There are 21 terms between the first and last terms. Find the a list of these intermediate terms.

• A
• B
• C
• D
• E

Q8:

Find the arithmetic sequence whose twentieth term is 28, given that the sum of its third and sixth terms is greater than its ninth term by 8.

• A
• B
• C
• D

Q9:

Find the arithmetic sequence in which the sum of the third and fourth terms equals , and exceeds by 8.

• A
• B
• C
• D

Q10:

Find the finite sequence , given and the twelfth-to-last term is .

• A
• B
• C
• D
• E

Q11:

Find the arithmetic sequence given and all terms are positive.

• A
• B
• C
• D
• E

Q12:

Find the arithmetic sequence given the sum of the second and fourth means is 198 and the seventh mean is greater than the third mean by 56.

• A
• B
• C
• D

Q13:

Find the value of the first negative term in an arithmetic sequence in which and .

Q14:

Determine the arithmetic sequence in which and .

• A
• B
• C
• D
• E

Q15:

Find the arithmetic sequence whose sixth term is 96 and the ratio between the fourth and tenth terms is .

• A
• B
• C
• D
• E

Q16:

Find the arithmetic sequence in which the sum of the second and third terms is , and the sum of their squares is 97.

• A or
• B or
• C or
• D or

Q17:

Find the increasing arithmetic sequence given and .

• A
• B
• C
• D
• E

Q18:

Find the arithmetic sequence given the sum of the fifth and tenth terms is , and the seventh term is 4 times greater than the fourth term.

• A
• B
• C
• D

Q19:

Find the arithmetic sequence given the fourth term is 42 and the sum of the fifth and ninth terms is 12. Then find the order of the term whose value is in this sequence.

• A
• B
• C
• D

Q20:

Find the arithmetic sequence given and . Then find the order and the value of the first term that exceeds 64.

• A, , 67
• B, ,
• C, ,
• D, , 67

Q21:

Find the sequence and its general term of all the even numbers greater than 62.

• A,
• B,
• C,
• D,

Q22:

Find the arithmetic sequence in which and the arithmetic mean of the third and sixth terms is .

• A
• B
• C
• D
• E