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(12,17,22,27,32)
  • B(9,11,13,15,17)
  • C(7,9,13,17,19)
  • D(7,9,11,13,15)
  • E343,473,20,733,863

Q6:

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

  • A𝑎=24, 𝑏=54, 𝑐=84
  • B𝑎=54, 𝑏=64, 𝑐=44
  • C𝑎=34, 𝑏=54, 𝑐=74
  • D𝑎=31, 𝑏=48, 𝑐=65

Q7:

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

Q8:

Evaluate the arithmetic mean between 77 and 24.

  • A101
  • B1,848
  • C532
  • D53
  • E2462

Q9:

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

  • A84,168
  • B86,166
  • C82,170
  • D1,2

Q10:

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

  • A16,601
  • B14,631
  • C56,11
  • D1,616

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.

  • A40,97
  • B20.25,57.5
  • C28,70
  • D26,72
  • E27,71

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.

  • A53,101
  • B37,117
  • C6.5,70.5
  • D89,25
  • E45,109

Q15:

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

  • A7𝑥+15
  • B7𝑥15
  • C14𝑥+30
  • D14𝑥30

Q16:

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

  • A𝑥=12 or 125
  • B𝑥=1 or 65
  • C𝑥=52 or 13
  • D𝑥=25 or 3
  • E𝑥=25 or 3

Q17:

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

  • A2, 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,).

  • A𝑥=2318, 𝑦=134
  • B𝑥=4318, 𝑦=94
  • C𝑥=6118, 𝑦=154
  • D𝑥=2918, 𝑦=154

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.

  • A272
  • B812
  • C33
  • D332
  • E67

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.

  • A22,33,,1011logloglog
  • Blogloglog2,22,,102
  • C22,32,,92logloglog
  • Dlogloglog3,23,,103

Q23:

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

  • A80
  • B40
  • C798
  • D2399
  • E45

Q24:

Find the arithmetic mean between log18 and log25.

  • A152
  • Blog432
  • C432
  • Dlog152
  • Elog450

Q25:

Insert 24 arithmetic means between log6 and log6.

  • A(12,18,24,,150)loglogloglog
  • B(26,36,46,,256)loglogloglog
  • C2,3,4,,25loglogloglog
  • D(62,63,64,,625)loglogloglog
  • E6,6,6,,6

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