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 1 1 2 4 5 .

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 9 3 4 7 .

Q5:

If 𝑛 arithmetic means are inserted between 1 0 8 and 5 6 , where the fourth mean exceeds the sum of the two means whose orders are ( 𝑛 2 ) and ( 𝑛 4 ) by 52, determine 𝑛 .

Q6:

Insert 5 arithmetic means between 7 and 19.

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

Q7:

Find 𝑎 , 𝑏 , and 𝑐 given the arithmetic sequence 𝑎 , 4 4 , 𝑏 , 6 4 , 𝑐 .

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

Q8:

The arithmetic mean between 4 5 and 𝑚 is 24. Find 𝑚 .

Q9:

Evaluate the arithmetic mean between 7 7 and 24.

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

Q10:

Find the two numbers whose arithmetic mean is 126, given the ratio between them is 1 2 .

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

Q11:

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

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

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

Q14:

Find the last arithmetic mean when 27 means are inserted between 8 6 and 5 8 .

Q15:

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

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

Q16:

Find, in terms of 𝑥 , the arithmetic mean of the two numbers 8 𝑥 + 8 and 6 𝑥 + 2 2 .

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

Q17:

An arithmetic sequence is 3 0 𝑥 9 , 5 𝑥 2 , 4 𝑥 7 , 2 . Find the value of 𝑥 .

  • A 𝑥 = 5 2 or 1 3
  • B 𝑥 = 2 5 or 3
  • C 𝑥 = 1 or 6 5
  • D 𝑥 = 2 5 or 3
  • E 𝑥 = 1 2 or 1 2 5

Q18:

Find all the possible values of 𝑥 that make 9 𝑥 , 1 4 , 𝑥 + 6 an arithmetic sequence.

  • A 2 , 11
  • B3, 1 0
  • C1, 1 2
  • D2, 1 1

Q19:

Find the values of 𝑥 and 𝑦 given the arithmetic sequence ( 9 𝑥 , 4 𝑦 + 1 , 2 𝑦 6 , 4 𝑦 + 2 , ) .

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

Q20:

Find 𝑐 , given the arithmetic sequence ( 𝑎 , 3 7 , 𝑏 , 6 1 , 𝑐 ) .

Q21:

Find the arithmetic mean between 𝑇 8 and 𝑇 1 1 for the arithmetic sequence 𝑇 = 3 𝑛 1 2 𝑛 .

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

Q22:

Find the arithmetic sequence in which 𝑇 = 2 𝑇 + 4 4 1 5 and the arithmetic mean of the third and sixth terms is 3 5 .

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

Q23:

The numbers 5 × 𝐶 2 0 𝑟 + 1 , 4 0 × 𝐶 2 0 𝑟 , and 3 9 × 𝐶 2 0 𝑟 1 form an arithmetic sequence. What is 𝑟 ?

Q24:

Find the eight arithmetic means between l o g 2 and l o g 1 0 2 4 .

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

Q25:

The sequence ( 4 2 , 𝑥 , 3 8 , ) l o g l o g l o g is an arithmetic sequence. What are the possible values of 𝑥 if 𝑥 + ?

  • A798
  • B40
  • C 4 5
  • D 2 3 9 9
  • E80

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