Insert into GP

Between numbers 5 and 640 insert as many numbers to form geometric progression so sum of the numbers you entered will be 630. How many numbers you must insert?

Result

m =  6

Solution:

a1=5 an=640 sn=630+640+5=1275 an=a1qn1 sn=qn1q1  128=qn1=qn/q 1275=qn1q1  1275=5128q1q1 1275q1275=5(128q1) 635q=1270 q=2  128=qn1 ln128=(n1)ln2 n=8  m=n2=82=6a_1 = 5 \ \\ a_n = 640 \ \\ s_n = 630+640+5 = 1275 \ \\ a_n= a_1 q^{n-1} \ \\ s_n= \dfrac{q^n-1}{q-1} \ \\ \ \\ 128 = q^{n-1} = q^n/q \ \\ 1275= \dfrac{q^n-1}{q-1} \ \\ \ \\ 1275= 5\cdot \dfrac{ 128 q - 1}{q-1} \ \\ 1275q - 1275 = 5\cdot (128 q - 1) \ \\ 635q = 1270 \ \\ q= 2 \ \\ \ \\ 128 = q^{n-1} \ \\ \ln 128 = (n-1) \ln 2 \ \\ n = 8 \ \\ \ \\ m = n-2 = 8-2 = 6



Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!





Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




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

Following knowledge from mathematics are needed to solve this word math problem:

Next similar math problems:

  1. Linear imaginary equation
    cplx_function Given that ? "this is z star" Find the value of the complex number z.
  2. Five harvests
    zrno In the seed company, they know that, out of 100 grains of a new variety, they get an average of 2000 grains after harvest. Approximately how many grains do they get out of 100 grains after five harvests?
  3. Sequence
    mandlebrot Find the common ratio of the sequence -3, -1.5, -0.75, -0.375, -0.1875. Ratio write as decimal number rounded to tenth.
  4. Geometric progression 2
    exp_x There is geometric sequence with a1=5.7 and quotient q=-2.5. Calculate a17.
  5. Six terms
    sequence_geo_3 Find the first six terms of the sequence a1 = -3, an = 2 * an-1
  6. Geometric sequence 5
    sequence About members of geometric sequence we know: ? ? Calculate a1 (first member) and q (common ratio or q-coefficient)
  7. Tenth member
    10 Calculate the tenth member of geometric sequence when given: a1=1/2 and q=2
  8. Five members
    pst3.JPG Write first 5 members geometric sequence and determine whether it is increasing or decreasing: a1 = 3 q = -2
  9. 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).
  10. A perineum
    sequence_geo_9 A perineum string is 10% shorter than its original string. The first string is 24, what is the 9th string or term?
  11. GP - 8 items
    fn Determine the first eight members of a geometric progression if a9=512, q=2
  12. Geometric progression 4
    square_rot_1 8,4√2,4,2√2
  13. Theorem prove
    thales_1 We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
  14. Ball game
    lopta_3 Richard, Denis and Denise together scored 932 goals. Denis scored 4 goals over Denise but Denis scored 24 goals less than Richard. Determine the number of goals for each player.
  15. Asymptote
    asymptote What is the vertical asymptote of ?
  16. Intercept with axis
    log_10 F(x)=log(x+4)-2, what is the x intercept
  17. Solve 3
    eq2_4 Solve quadratic equation: (6n+1) (4n-1) = 3n2