# Lesson Worksheet: Using Arithmetic Sequence Formulas Mathematics • 9th Grade

In this worksheet, we will practice writing explicit and recursive formulas for arithmetic sequences to find the value of the 𝑛th term in an arithmetic sequence and finding a term’s order given its value.

Q1:

Fill in the blank: If the first term of an arithmetic sequence equals 16 and , then the fifth term equals .

Q2:

Find, in terms of , the general term of the arithmetic sequence .

• A
• B
• C
• D
• E

Q3:

Using the table, determine the expression that represents the value of each term as a function of its position. Then, find the value of the eighteenth term in the sequence.

 Position Value of Term 6 7 8 9 𝑛 19 22 25 28 ⋯
• A, 22
• B, 54
• C, 24
• D, 55
• E, 53

Q4:

Find in the arithmetic sequence .

• A
• B
• C
• D

Q5:

Find the general term of the arithmetic sequence which satisfies the relations and .

• A
• B
• C
• D
• E

Q6:

Find the number of terms in the arithmetic sequence .

Q7:

Find the order of the term whose value is 112 in the sequence .

• A
• B
• C
• D

Q8:

Find the first three terms in the sequence which has general term and . Then find the order of the term whose value is 157 and the order of the first term whose value is more than 100.

• A, ,
• B, ,
• C, ,
• D, ,

Q9:

Find the term of the arithmetic sequence given that and . Then find the position and value of the first negative term in the sequence.

• A, 7, 5
• B, 7,
• C, 8,
• D, 8, 5

Q10:

Find and the number of terms in the arithmetic sequence .

• A
• B
• C
• D