Sum of GP members

Determine the sum of the GP 30, 6, 1.2, to 5 terms. What is the sum of all terms (to infinity)?

Correct result:

s5 =  37.488
s =  37.5

Solution:

a1=30 a2=6 a3=1.2  r=a2/a1=6/30=15=0.2 r2=a3/a2=1.2/6=15=0.2 r=r2 a4=a3⋅ r=1.2⋅ 0.2=625=0.24 a5=a4⋅ r=0.24⋅ 0.2=6125=0.048  s5=a1+a2+a3+a4+a5=30+6+1.2+0.24+0.048=4686125=37.488
s=a1⋅ 11−r=30⋅ 11−0.2=752=37.5

Try another example


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




You need to know the following knowledge to solve this word math problem:

Next similar math problems:

  • 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 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?
  • Sum of series
    question Determine the 6-th member and the sum of a geometric series: 5-4/1+16/5-64/25+256/125-1024/625+....
  • Infinity
    circles-and-squares In a square with side 19 is inscribed circle, the circle is inscribed next square, again circle, and so on to infinity. Calculate the sum of the area of all these squares.
  • Geometric progression
    exp_1 In geometric progression, a1 = 7, q = 5. Find the condition for n to sum first n members is: sn≤217.
  • What are 2
    seq What are the two more terms of the GP a, ax, ax2, ax3, __, __?
  • Infinite sum of areas
    height-of-equilateral-triangle Above the height of the equilateral triangle ABC is constructed an equilateral triangle A1, B1, C1, of the height of the equilateral triangle built A2, B2, C2, and so on. The procedure is repeated continuously. What is the total sum of the areas of all tr
  • Population growth
    exp_growth How many people will be on Earth from two people for 5,000 years, if every couple has always 4 children, (2 boys and 2 girls) at the age of 25-35, and every man will live 75 years?
  • GP members
    sequence_geo_8 The geometric sequence has 10 members. The last two members are 2 and -1. Which member is -1/16?
  • 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.
  • 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.
  • 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.
  • Geometric seq
    eq222_1 Find the third member of geometric progression if a1 + a2 = 36 and a1 + a3 = 90. Calculate its quotient.
  • Infinite decimal
    series Imagine the infinite decimal number 0.99999999 .. ... ... ... That is a decimal and her endless serie of nines. Determine how much this number is less than the number 1. Thank you in advance.
  • Harmonic series
    mean_normal Insert four members between 5/3 and 5/11 to form harmonic series (means).
  • 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.
  • Series and sequences
    seq_sum Find a fraction equivalent to the recurring decimal? 0.435643564356