Cinema 4

In cinema are 1656 seats and in the last row are 105 seats , in each next row 3 seats less. How many are the total rows in cinema?

Correct result:

n =  23

Solution:

1. a(1) = 105; S(1) = 105
2. a(2) = 102; S(2) = 207
3. a(3) = 99; S(3) = 306
4. a(4) = 96; S(4) = 402
5. a(5) = 93; S(5) = 495
6. a(6) = 90; S(6) = 585
7. a(7) = 87; S(7) = 672
8. a(8) = 84; S(8) = 756
9. a(9) = 81; S(9) = 837
10. a(10) = 78; S(10) = 915
11. a(11) = 75; S(11) = 990
12. a(12) = 72; S(12) = 1062
13. a(13) = 69; S(13) = 1131
14. a(14) = 66; S(14) = 1197
15. a(15) = 63; S(15) = 1260
16. a(16) = 60; S(16) = 1320
17. a(17) = 57; S(17) = 1377
18. a(18) = 54; S(18) = 1431
19. a(19) = 51; S(19) = 1482
20. a(20) = 48; S(20) = 1530
21. a(21) = 45; S(21) = 1575
22. a(22) = 42; S(22) = 1617
23. a(23) = 39; S(23) = 1656

sn=1656 a1=105 d=3  sn=n(a1+an)/2=n(a1+a1+(n1)d)/2 1656=n/2(21053(n1)) 3312=n(2133n) 3312=213n3n2 3n2213n+3312=0 n1,2=b±D2a=213±56256 n1,2=213±756 n1,2=35.5±12.5 n1=48 n2=23 n=23



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?

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

Next similar math problems:

  • Discriminant
    Quadratic_equation_discriminant Determine the discriminant of the equation: ?
  • Equation 23
    reciprocal_1 Find value of unknown x in equation: x+3/x+1=5 (problem finding x)
  • What is 9
    seq What is the 15th term; x1=1.5, d=4.5?
  • Equation
    calculator_2 Equation ? has one root x1 = 8. Determine the coefficient b and the second root x2.
  • The product
    eq222 The product of a number plus that number and its inverse is two and one-half. What is the inverse of this number
  • Quadratic inequation
    eq2_8 If 5x + x² > 100, then x is not
  • Quadratic equation
    Parabola_tangent Quadratic equation ? has roots x1 = -26 and x2 = -86. Calculate the coefficients b and c.
  • Sequence
    sunflower Between numbers 1 and 53 insert n members of the arithmetic sequence that its sum is 702.
  • Solve 3
    eq2_4 Solve quadratic equation: (6n+1) (4n-1) = 3n2
  • Roots
    parabola Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
  • Quadratic equation
    kvadrat_2 Find the roots of the quadratic equation: 3x2-4x + (-4) = 0.
  • Find the 20
    eq222_1 Find the product and the sum of the roots of x2 + 3x - 9 = 0
  • AS sequence
    AP In an arithmetic sequence is given the difference d = -3 and a71 = 455. a) Determine the value of a62 b) Determine the sum of 71 members.
  • Find d 2
    lines Find d in an A. P. whose 5th term is 18 and 39th term is 120.
  • Sequence 3
    75 Write the first 5 members of an arithmetic sequence: a4=-35, a11=-105.
  • 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
  • Tubes
    pipes_1 Iron tubes in the warehouse are stored in layers so that each tube top layer fit into the gaps of the lower layer. How many layers are needed to deposit 100 tubes if top layer has 9 tubes? How many tubes are in bottom layer of tubes?