Geometric progression 4

8,4√2,4,2√2

Correct answer:

q =  0.7071
a₅ =  2
a₆ =  1.4142
a₇ =  1

Step-by-step explanation:

$$\begin{gathered} a_1=8 \\ {a}_2=4\cdot \sqrt{2}=4\sqrt{2}\doteq 5.6569 \\ {a}_3=4 \\ {a}_4=2\cdot \sqrt{2}=2\sqrt{2}\doteq 2.8284 \\ {q}_1=a_2\mathrm{/}{a}_1=5.6569\mathrm{/}8\doteq 0.7071 \\ {q}_2=a_3\mathrm{/}{a}_2=4\mathrm{/}5.6569\doteq 0.7071 \\ {q}_3=a_4\mathrm{/}{a}_3=2.8284\mathrm{/}4\doteq 0.7071 \\ {q}_1=q_2=q_3 \\ q=q_3=0.7071=0.7071 \end{gathered}$$

$a_5=q\cdot a_4=0.7071\cdot 2.8284=2$

$a_6=q\cdot a_5=0.7071\cdot 2=\sqrt{2}=1.4142$

$a_7=q\cdot a_6=0.7071\cdot 1.4142=1$

Try another example

Related math problems and questions:

• Geometric progression
  Fill 4 numbers between 4 and -12500 to form geometric progression.
• Coefficient
  Determine the coefficient of this sequence: 7.2; 2.4; 0.8
• Geometric progression 2
  There is geometric sequence with a₁=5.7 and quotient q=-2.5. Calculate a₁₇.
• GP - 8 items
  Determine the first eight members of a geometric progression if a₉=512, q=2
• Gp - 80
  One of the first four members of a geometric progression is 80. Find its if we know that the fourth member is nine times greater than the second.
• Insert
  Insert five numbers between 8 and 27 such numbers that, with two given ones, they form the first seven members of the geometric sequence.
• HP - harmonic progression
  Determine the 8th term of the harmonic progression 2, 4/3, 1,…
• Geometric sequence 3
  In geometric sequence is a₈ = 312500; a₁₁= 39062500; s_n=1953124. Calculate the first item a₁, quotient q, and n - number of members by their sum s_n.
• Geometric sequence
  In the geometric sequence is a₄ = 20 a₉ = -160. Calculate the first member a₁ and quotient q.
• Square area
  Complete the table and then draw each square. Provide exact lengths. Describe any problems you have. Side Length Area Square 1 1 unit² Square 2 2 units² Square 3 4 units²
• If the 3
  If the 6th term of a GP is 4 and the 10th is 4/81, find common ratio r.
• Geometric progression
  In geometric progression, a1 = 7, q = 5. Find the condition for n to sum first n members is sn≤217.
• Geometric mean
  Calculate the geometric mean of numbers a=15.2 and b=25.6. Determine the mean by construction where a and b are the length of the lines.
• Missing term 2
  What is the missing term for the Geometric Progression (GP) 3, 15, 75,__, 1875?
• Quotient
  Determine the quotient and the second member of the geometric progression where a3=10, a1+a2=-1,6 a1-a2=2,4.
• Six speeds
  A drilling machine is to have 6 speeds ranging from 50 to 750 revolutions per minute. If the speed forms a geometric progression, determine their values.
• In the
  In the arithmetic sequence a1 = 4.8, d = 0.4. How many consecutive members, starting with the first, need to be added so that the sum is greater than 170?