Insert 3

Insert five arithmetic progression members between -7 and 3/2.

Correct answer:

a₂ =  -5.5833
a₃ =  -4.1667
a₄ =  -2.75
a₅ =  -1.3333
a₆ =  0.0833

Step-by-step explanation:

$$\begin{gathered} a_1=-7 \\ {a}_7=3\mathrm{/}2={\displaystyle \frac{3}{2}}=1\frac{1}{2}=1.5 \\ {a}_7=a_1+6d \\ d=(a_7-a_1)\mathrm{/}6=(1.5-(-7))\mathrm{/}6={\displaystyle \frac{17}{12}}=1\frac{5}{12}\doteq 1.4167 \\ {a}_2=a_1+d=(-7)+1.4167=-{\displaystyle \frac{67}{12}}=-5\frac{7}{12}=-5.5833 \end{gathered}$$

$a_3=a_2+d=(-5.5833)+1.4167=-{\displaystyle \frac{25}{6}}=-4\frac{1}{6}=-4.1667$

$a_4=a_3+d=(-4.1667)+1.4167=-{\displaystyle \frac{11}{4}}=-2\frac{3}{4}=-2.75$

$a_5=a_4+d=(-2.75)+1.4167=-{\displaystyle \frac{4}{3}}=-1\frac{1}{3}=-1.3333$

$a_6=a_5+d=(-1.3333)+1.4167=0.0833$

Try another example

Related math problems and questions:

• Insert 7
  Insert five harmonic means between 3 and 18
• Harmonic series
  Insert four members between 5/3 and 5/11 to form harmonic series (means).
• Insert 6
  Insert four harmonic means between 3/7 and 3/19
• Negative difference
  Find four arithmetic progression members between 7 and -6.
• Sequence
  Between numbers 1 and 53 insert n members of the arithmetic sequence that its sum is 702.
• Insert 4
  Insert 3 arithmetic means between 3 and 63.
• GP members
  The geometric sequence has 10 members. The last two members are 2 and -1. Which member is -1/16?
• Insert 5
  Insert five harmonic means between 1/2 and 1/26
• Five element
  The geometric sequence is given by quotient q = 1/2 and the sum of the first six members S₆ = 63. Find the fifth element a₅.
• HP - harmonic progression
  Determine the 8th term of the harmonic progression 2, 4/3, 1,…
• Geometric progression
  In geometric progression, a1 = 7, q = 5. Find the condition for n to sum first n members is: sn≤217.
• Sum of members
  What is the sum of the first two members of the aritmetic progression if d = -4.3 and a3 = 7.5?
• Fifth member
  Determine the fifth member of the arithmetic progression, if the sum of the second and fifth members equal to 73, and difference d = 7.
• Arithmetic progression 2
  The 3rd term of an Arithmetic progression is ten more than the first term, while the fifth term is 15 more than the second term. Find the sum of the 8th and 15th terms of the Arithmetic progression if the 7th term is seven times the first term.
• Find unknown 2
  Find unknown denominator: 2/3 -5/? = 1/4
• Five members
  Write first 5 members geometric sequence and determine whether it is increasing or decreasing: a₁ = 3 q = -2
• Insert into GP
  Between numbers 5 and 640, insert as many numbers to form geometric progression so the sum of the numbers you entered will be 630. How many numbers must you insert?