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 geometric sequences, but with the same two members)

Correct answer:

n =  4
q =  4
n2 =  7
q2 =  -2

Step-by-step explanation:

a1=6 an=384 sn=510  sn=a1 qn1q1 an=a1 qn/q  sn=a1 an/a1 q1q1  sn (q1)=a1 (an/a1 q1) 510 (q1)=6 (384/6 q1)  756q=3024  q=4  n=log(an/a1 q)/log(q)=log(384/6 4)/log(4)=4
s2=132+a1+an=132+6+384=258  s2 (q21)=a1 (an/a1 q21) 258 (q21)=6 (384/6 q21)  756q2=1512  q2=2  n2=7   Verifying Solution:  b1=a1=6 b2=b1 q2=6 (2)=12 b3=b2 q2=(12) (2)=24 b4=b3 q2=24 (2)=48 b5=b4 q2=(48) (2)=96 b6=b5 q2=96 (2)=192 b7=b6 q2=(192) (2)=384 b7=an  S2=b2+b3+b4+b5+b6=(12)+24+(48)+96+(192)=132  n2=log(an/a1 q2)/log(q2)=7

Did you find an error or inaccuracy? Feel free to write us. Thank you!


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

Related math problems and questions:

  • Insert into GP
    archimedes 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?
  • Geometric progression
    exp In geometric progression, a1 = 7, q = 5. Find the condition for n to sum first n members is sn≤217.
  • Crystal
    crystal The crystal grows every month 1.2 permille of its mass. For how many months to grow a crystal from weight 177 g to 384 g?
  • Three members GP
    exp_growth The sum of three numbers in GP (geometric progression) is 21 and the sum of their squares is 189. Find the numbers.
  • Sum of GP members
    exponentialFexsDecay Determine the sum of the GP 30, 6, 1.2, to 5 terms. What is the sum of all terms (to infinity)?
  • 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.
  • 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 the value of c.
  • Remainders
    dividing It is given a set of numbers { 170; 244; 299; 333; 351; 391; 423; 644 }. Divide this numbers by number 66 and determine set of remainders. As result write sum of this remainders.
  • GP members
    sequence_geo The geometric sequence has 10 members. The last two members are 2 and -1. Which member is -1/16?
  • A book
    books A book contains 524 pages. If it is known that a person will select any one page between the pages numbered 125 and 384, find the probability of choosing the page numbered 252 or 253.
  • Sequence
    sunflower Between numbers 1 and 53 insert n members of the arithmetic sequence that its sum is 702.
  • Concert
    freddie-mercury On a Concert were sold 150 tickets for CZK 360, 235 tickets for 240 CZK and 412 for 180 CZK. How much was the total revenues for tickets?
  • If the 3
    sequence_geo If the 6th term of a GP is 4 and the 10th is 4/81, find common ratio r.
  • Insert 3
    arithmet_seq Insert five arithmetic progression members between -7 and 3/2.
  • Exponential equation
    exp Find x, if 625 ^ x = 5 The equation is exponential because the unknown is in the exponential power of 625
  • Five element
    sequence_geo 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.
  • Chickens and rabbits
    pipky In the yard were chickens and rabbits. Together they had 18 heads and 56 legs. How many chickens and how many rabbits were in the yard?