If the 3

If the 6th term of a GP is 4 and the 10th is 4/81, find common ratio r.

Correct answer:

r =  0.3333

Step-by-step explanation:

$$\begin{gathered} a_6=4 \\ {a}_{10}={\displaystyle \frac{4}{81}}={\displaystyle \frac{4}{81}}\doteq 0.0494 \\ {a}_{10}=a_6\cdot r^{10-6} \\ r=\sqrt[4]{a_{10}\mathrm{/}{a}_6}=\sqrt[4]{0.0494\mathrm{/}4}={\displaystyle \frac{1}{3}}=0.3333 \end{gathered}$$

Try another example

Related math problems and questions:

• What is 10
  What is the 5th term, if the 8th term is 80 and common ratio r =1/2?
• Three members GP
  The sum of three numbers in GP (geometric progression) is 21 and the sum of their squares is 189. Find the numbers.
• 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.
• Terms of GP
  What is the 6th term of the GP 9, 81, 729,. .. ?
• Find the 19
  Find the 1st term of the GP ___, -6, 18, -54.
• Geometric progressiob
  If the sum of four consective terms of geometric progression is 80 and arithmetic mean of second and fourth term is 30 then find terms?
• Common difference
  The 4th term of an arithmetic progression is 6. If the sum of the 8th and 9th terms is -72, find the common difference.
• Two geometric progressions
  Insert several numbers between numbers 6 and 384 so that they form with the given GP numbers and that the following applies: a) the sum of all numbers is 510 And for another GP to apply: b) the sum of entered numbers is -132 (These are two different geome
• 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.
• 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.
• GP members
  The geometric sequence has 10 members. The last two members are 2 and -1. Which member is -1/16?
• HP - harmonic progression
  Determine the 8th term of the harmonic progression 2, 4/3, 1,…
• GP - three members
  The second and third of a geometric progression are 24 and 12(c+1), respectively, given that the sum of the first three terms of progression is 76. determine the value of c.
• Missing term 2
  What is the missing term for the Geometric Progression (GP) 3, 15, 75,__, 1875?
• Sequences AP + GP
  The three numbers that make up the arithmetic sequence have the sum of 30. If we subtract from the first 5, from the second 4 and keep the third, we get the geometric sequence. Find AP and GP members.
• HP - harmonic progression 2
  Compute the 16th term of the HP if the 6th and 11th term of the harmonic progression are 10 and 18 respectively.
• HP - harmonic progression
  Determine the 10th term of the harmonic progression 6,4,3,…