# 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 terms inserted between 2 and 104 given the sum of the fifteenth and twentieth term is 109.

**Q4: **

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

**Q5: **

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 .

**Q6: **

Insert 5 arithmetic means between 7 and 19.

- A
- B
- C
- D
- E

**Q8: **

The arithmetic mean between and is 24. Find .

**Q9: **

Evaluate the arithmetic mean between and 24.

- A101
- B
- C
- D
- E

**Q10: **

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

- A
- B
- C
- D

**Q11: **

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

- A
- B
- C
- D

**Q12: **

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

**Q13: **

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

- A
- B
- C
- D
- E

**Q14: **

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

**Q15: **

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

- A
- B
- C
- D
- E

**Q16: **

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

- A
- B
- C
- D

**Q17: **

An arithmetic sequence is . Find the value of .

- A or
- B or
- C or
- D or 3
- E or

**Q18: **

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

- A , 11
- B3,
- C1,
- D2,

**Q19: **

Find the values of and given the arithmetic sequence .

- A ,
- B ,
- C ,
- D ,

**Q20: **

Find , given the arithmetic sequence .

**Q21: **

Find the arithmetic mean between and for the arithmetic sequence .

- A
- B
- C
- D
- E

**Q22: **

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

- A
- B
- C
- D
- E

**Q23: **

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

**Q24: **

Find the eight arithmetic means between and .

- A
- B
- C
- D

**Q25: **

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

- A798
- B40
- C
- D
- E80