Geometric sequence 4

It is given geometric sequence a3 = 7 and a12 = 3. Calculate s23 (= sum of the first 23 members of the sequence).

Result

s23 =  83.26

Solution:

a3=a1q31=7 a12=a1q121=3  3/7=q123=q9 q=3/79=0.9102  a10.910231=7 a1=7/0.910231=8.4503  s23=a1q231q1=8.45030.91022310.91021=83.26a_{ 3 } = a_1 q^{ 3-1} = 7 \ \\ a_{ 12 } = a_1 q^{ 12-1} = 3 \ \\ \ \\ 3/7 = q^ { 12 - 3 } = q^{ 9} \ \\ q = \sqrt[ 9 ]{ 3/7 } = 0.9102 \ \\ \ \\ a_1 0.9102^{ 3-1} = 7 \ \\ a_1 = 7 / 0.9102^{ 3-1} = 8.4503 \ \\ \ \\ s_{ 23 } = a_1 \dfrac{q^{ 23 } -1 }{q-1} = 8.4503 \dfrac{ 0.9102^{ 23 } -1 }{ 0.9102-1} = 83.26



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




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

Next similar math problems:

  1. Tenth member
    10 Calculate the tenth member of geometric sequence when given: a1=1/2 and q=2
  2. Geometric progression 2
    exp_x There is geometric sequence with a1=5.7 and quotient q=-2.5. Calculate a17.
  3. Five members
    pst3.JPG Write first 5 members geometric sequence and determine whether it is increasing or decreasing: a1 = 3 q = -2
  4. Six terms
    sequence_geo_3 Find the first six terms of the sequence a1 = -3, an = 2 * an-1
  5. GP members
    sequence_geo_8 The geometric sequence has 10 members. The last two members are 2 and -1. Which member is -1/16?
  6. 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.
  7. GP - 8 items
    fn Determine the first eight members of a geometric progression if a9=512, q=2
  8. 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?
  9. Quotient
    fun1_1 Determine the quotient and the second member of the geometric progression where a3=10, a1+a2=-1,6 a1-a2=2,4.
  10. Computer
    pc The computer was purchased 10000,-. Each year, the price of a computer depreciates always the same percentage of the previous year. After four years, the value of the computer is reduced to 1300,- How many percent was depreciated price of the computer each
  11. The city 2
    kingkong Today lives 167000 citizens in city. How many citizens can we expect in 11 years if their annual increase is 1%?
  12. Machine
    machine Price of the new machine is € 62000. Every year is depreciated 15% of residual value. What will be the value of the machine after 3 years?
  13. Geometric progression 4
    square_rot_1 8,4√2,4,2√2
  14. 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?
  15. Seats
    divadlo_2 Seats in the sport hall are organized so that each subsequent row has five more seats. First has 10 seats. How many seats are: a) in the eighth row b) in the eighteenth row
  16. Value
    5times_1 Find the value of the expression: 6!·10^-3
  17. 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?