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 4 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 11245.

Q3:

Find the number of arithmetic means inserted between 194 and 90 given the ratio between the second and the last means is 9347.

Q4:

If 𝑛 arithmetic means are inserted between 108 and 56, where the fourth mean exceeds the sum of the two means whose orders are (𝑛2) and (𝑛4) by 52, determine 𝑛.

Q5:

Find 5 arithmetic means between 7 and 19.

  • A ( 1 2 , 1 7 , 2 2 , 2 7 , 3 2 )
  • B ( 9 , 1 1 , 1 3 , 1 5 , 1 7 )
  • C ( 7 , 9 , 1 3 , 1 7 , 1 9 )
  • D ( 7 , 9 , 1 1 , 1 3 , 1 5 )
  • E 3 4 3 , 4 7 3 , 2 0 , 7 3 3 , 8 6 3

Q6:

Find 𝑎, 𝑏, and 𝑐 given the arithmetic sequence 𝑎,44,𝑏,64,𝑐.

  • A 𝑎 = 2 4 , 𝑏 = 5 4 , 𝑐 = 8 4
  • B 𝑎 = 5 4 , 𝑏 = 6 4 , 𝑐 = 4 4
  • C 𝑎 = 3 4 , 𝑏 = 5 4 , 𝑐 = 7 4
  • D 𝑎 = 3 1 , 𝑏 = 4 8 , 𝑐 = 6 5

Q7:

The arithmetic mean between 45 and 𝑚 is 24. Find 𝑚.

Q8:

Evaluate the arithmetic mean between 77 and 24.

  • A101
  • B 1 , 8 4 8
  • C 5 3 2
  • D 5 3
  • E 2 4 6 2

Q9:

Find the two numbers whose arithmetic mean is 126, given the ratio between them is 12.

  • A 8 4 , 1 6 8
  • B 8 6 , 1 6 6
  • C 8 2 , 1 7 0
  • D 1 , 2

Q10:

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

  • A 1 6 , 6 0 1
  • B 1 4 , 6 3 1
  • C 5 6 , 1 1
  • D 1 , 6 1 6

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 4 0 , 9 7
  • B 2 0 . 2 5 , 5 7 . 5
  • C 2 8 , 7 0
  • D 2 6 , 7 2
  • E 2 7 , 7 1

Q13:

Find the last arithmetic mean when 27 means are inserted between 86 and 58 .

Q14:

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

  • A 5 3 , 1 0 1
  • B 3 7 , 1 1 7
  • C 6 . 5 , 7 0 . 5
  • D 8 9 , 2 5
  • E 4 5 , 1 0 9

Q15:

Find, in terms of 𝑥, the arithmetic mean of the two numbers 8𝑥+8 and 6𝑥+22.

  • A 7 𝑥 + 1 5
  • B 7 𝑥 1 5
  • C 1 4 𝑥 + 3 0
  • D 1 4 𝑥 3 0

Q16:

An arithmetic sequence is 30𝑥9,5𝑥2,4𝑥7,. Find the value of 𝑥.

  • A 𝑥 = 1 2 or 125
  • B 𝑥 = 1 or 65
  • C 𝑥 = 5 2 or 13
  • D 𝑥 = 2 5 or 3
  • E 𝑥 = 2 5 or 3

Q17:

Find all the possible values of 𝑥 that make 9𝑥,14,𝑥+6 an arithmetic sequence.

  • A 2 , 11
  • B2, 11
  • C3, 10
  • D1, 12

Q18:

Find the values of 𝑥 and 𝑦 given the arithmetic sequence (9𝑥,4𝑦+1,2𝑦6,4𝑦+2,).

  • A 𝑥 = 2 3 1 8 , 𝑦 = 1 3 4
  • B 𝑥 = 4 3 1 8 , 𝑦 = 9 4
  • C 𝑥 = 6 1 1 8 , 𝑦 = 1 5 4
  • D 𝑥 = 2 9 1 8 , 𝑦 = 1 5 4

Q19:

Find 𝑐, given the arithmetic sequence (𝑎,37,𝑏,61,𝑐).

Q20:

Find the arithmetic mean between 𝑎 and 𝑎 for the arithmetic sequence 𝑎=3𝑛12.

  • A 2 7 2
  • B 8 1 2
  • C 3 3
  • D 3 3 2
  • E 6 7

Q21:

The numbers 5×𝐶, 40×𝐶, and 39×𝐶 form an arithmetic sequence. What is 𝑟?

Q22:

Find the eight arithmetic means between log2 and log1,024.

  • A 2 2 , 3 3 , , 1 0 1 1 l o g l o g l o g
  • B l o g l o g l o g 2 , 2 2 , , 1 0 2
  • C l o g l o g l o g 3 , 2 3 , , 1 0 3
  • D 2 2 , 3 2 , , 9 2 l o g l o g l o g

Q23:

The sequence (42,𝑥,38,)logloglog is an arithmetic sequence. What are the possible values of 𝑥 if 𝑥?

  • A80
  • B40
  • C798
  • D 2 3 9 9
  • E 4 5

Q24:

Find the arithmetic mean between log18 and log25.

  • A 1 5 2
  • B l o g 4 3 2
  • C 4 3 2
  • D l o g 1 5 2
  • E l o g 4 5 0

Q25:

Insert 24 arithmetic means between log6 and log6.

  • A ( 1 2 , 1 8 , 2 4 , , 1 5 0 ) l o g l o g l o g l o g
  • B ( 2 6 , 3 6 , 4 6 , , 2 5 6 ) l o g l o g l o g l o g
  • C 2 , 3 , 4 , , 2 5 l o g l o g l o g l o g
  • D ( 6 2 , 6 3 , 6 4 , , 6 2 5 ) l o g l o g l o g l o g
  • E 6 , 6 , 6 , , 6

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.