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.

Correct result:

a =  3
b =  6
c =  12
a2 =  12
b2 =  6
c2 =  3

Solution:

a+b+c=21 a2+b2+c2=189  b=qa c=q2a  a+qa+q2a=21 a2+q2a2+q4a2=189  a(1+q+q2)=21 a2(1+q2+q4)=189  212(1+q2+q4)=189(1+q+q2)2 252 q4378 q3126 q2378 q+252=0  q4+q2+1=(q2q+1) (q2+q+1)  212(q2q+1) (q2+q+1)=189(1+q+q2)2 212(q2q+1)=189(1+q+q2)  212(q2q+1)=189(1+q+q2) 252q2630q+252=0  a=252;b=630;c=252 D=b24ac=63024252252=142884 D>0  q1,2=b±D2a=630±142884504 q1,2=630±378504 q1,2=1.25±0.75 q1=2 q2=0.5   Factored form of the equation:  252(q2)(q0.5)=0   a=21/(1+q1+q12)=21/(1+2+22)=3

Our quadratic equation calculator calculates it.

b=q1 a=2 3=6b=q_{1} \cdot \ a=2 \cdot \ 3=6
c=q1 b=2 6=12c=q_{1} \cdot \ b=2 \cdot \ 6=12
a2=21/(1+q2+q22)=21/(1+0.5+0.52)=12a_{2}=21/(1+q_{2}+q_{2}^2)=21/(1+0.5+0.5^2)=12
b2=q2 a2=0.5 12=6b_{2}=q_{2} \cdot \ a_{2}=0.5 \cdot \ 12=6
c2=q2 b2=0.5 6=3c_{2}=q_{2} \cdot \ b_{2}=0.5 \cdot \ 6=3



We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!






Showing 0 comments:
avatar




Tips to related online calculators
Looking for help with calculating roots of a quadratic equation?
Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?

Next similar math problems:

  • Gp - 80
    gp_1 Sum of the first four members of a geometric progression is 80. Determine they if we know that the fourth member is nine times greater than the second.
  • Geometric progressiob
    eq2 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?
  • Geometric progression
    exp_1 In geometric progression, a1 = 7, q = 5. Find the condition for n to sum first n members is: sn≤217.
  • If the 3
    sequence_geo If the 6th term of a GP is 4 and the 10th is 4/81, find common ratio r.
  • Sequences AP + GP
    seq_sum 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.
  • The sum
    eq222_1 The sum of the squares of two immediately following natural numbers is 1201. Find these numbers.
  • Annual income
    income The annual incomes (in thousands of $) of fifteen families is: 60, 80, 90, 96, 120, 150, 200, 360, 480, 520, 1060, 1200, 1450, 2500, 7200 Calculate harmonic and geometric mean.
  • GP - three members
    progression_ao 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 value of c
  • Geometric sequence 3
    sequence In geometric sequence is a8 = 312500; a11= 39062500; sn=1953124. Calculate the first item a1, quotient q and n - number of members by their sum s_n.
  • Geometric sequence 4
    Koch_Snowflake_Triangles It is given geometric sequence a3 = 7 and a12 = 3. Calculate s23 (= sum of the first 23 members of the sequence).
  • Moivre 2
    moivre_complex Find the cube roots of 125(cos 288° + i sin 288°).
  • Geometric sequence
    cralici In the geometric sequence is a4 = 20 a9 = -160. Calculate the first member a1 and quotient q.
  • Six speeds
    gears-3 A drilling machine is to have 6 speed ranging from 50 to 750 revolution per minute. If the speed forms a geometric progression, determine their values.
  • Exponential equation
    exp Find x, if 625 ^ x = 5 The equation is exponential because the unknown is in the exponential power of 625
  • Recursion squares
    squares_reccurent In the square, ABCD has inscribed a square so that its vertices lie at the centers of the sides of the square ABCD. The procedure of inscribing the square is repeated this way. The side length of the square ABCD is a = 22 cm. Calculate: a) the sum of peri
  • Derivative problem
    derive The sum of two numbers is 12. Find these numbers if: a) The sum of their third powers is minimal. b) The product of one with the cube of the other is maximal. c) Both are positive and the product of one with the other power of the other is maximal.
  • The sum
    seq_sum The sum of the first 10 members of the arithmetic sequence is 120. What will be the sum if the difference is reduced by 2?