# Worksheet: Arithmetic Mean

In this worksheet, we will practice finding the arithmetic means for any two nonconsecutive terms in an arithmetic sequence.

Q1:

Find the number of the arithmetic means inserted between and 101 given the twelveth mean is 8 times the second one.

Q2:

Find the number of arithmetic means inserted between 2 and 254 given the ratio between the sum of the first two means and the sum of the last two means is .

Q3:

Find the number of arithmetic means inserted between 194 and 90 given the ratio between the second and the last means is .

Q4:

If arithmetic means are inserted between and , where the fourth mean exceeds the sum of the two means whose orders are and by 52, determine .

Q5:

Find 5 arithmetic means between 7 and 19.

• A
• B
• C
• D
• E

Q6:

Find , , and given the arithmetic sequence

• A, ,
• B, ,
• C, ,
• D, ,

Q7:

The arithmetic mean between and is 24. Find .

Q8:

Evaluate the arithmetic mean between and 24.

• A101
• B
• C
• D
• E

Q9:

Find the two numbers whose arithmetic mean is 126, given the ratio between them is .

• A
• B
• C
• D

Q10:

Find the two numbers whose arithmetic mean is 308.5 and product is 616.

• A
• B
• C
• D

Q11:

Find the number of arithmetic means inserted between 8 and 238 given the sum of the second and the sixth means is 96.

Q12:

Find the two numbers whose arithmetic mean is 49, where one number is 17 more than twice the other.

• A
• B
• C
• D
• E

Q13:

Find the last arithmetic mean when 27 means are inserted between and .

Q14:

Find the two numbers whose arithmetic mean is 77, and the difference between them is 64.

• A
• B
• C
• D
• E

Q15:

Find, in terms of , the arithmetic mean of the two numbers and .

• A
• B
• C
• D

Q16:

An arithmetic sequence is . Find the value of .

• A or
• B or
• C or
• D or 3
• E or

Q17:

Find all the possible values of that make an arithmetic sequence.

• A, 11
• B2,
• C3,
• D1,

Q18:

Find the values of and given the arithmetic sequence .

• A,
• B,
• C,
• D,

Q19:

Find , given the arithmetic sequence .

Q20:

Find the arithmetic mean between and for the arithmetic sequence .

• A
• B
• C
• D
• E

Q21:

The numbers , , and form an arithmetic sequence. What is ?

Q22:

Find the eight arithmetic means between and .

• A
• B
• C
• D

Q23:

The sequence is an arithmetic sequence. What are the possible values of if ?

• A80
• B40
• C798
• D
• E

Q24:

Find the arithmetic mean between and .

• A
• B
• C
• D
• E

Q25:

Insert 24 arithmetic means between and .

• A
• B
• C
• D
• E