Sequence

In the arithmetic sequence is given:

Sn=2304, d=2, an=95

Calculate a1 and n.

Correct result:

a =  1
n =  48

Solution:

s=2304 d=2 b=95  b=a+d⋅ (n−1) s=n⋅ (a+b)/2  a=b−d⋅ (n−1) 2s=n⋅ (a+b)  2s=n⋅ (b−d⋅ (n−1)+b)  2∗2304=n∗(2∗95−2∗(n−1))  2⋅ 2304=n⋅ (2⋅ 95−2⋅ (n−1)) 2n2−192n+4608=0  a=2;b=−192;c=4608 D=b2−4ac=1922−4⋅2⋅4608=0 D=0  n1,2=−b±D2a=192±04=48±0 n1,2=48±0 n1=n2=48    Factored form of the equation:  2(n−48)(n−48)=0  n>0 n=n1=48 a=b−d⋅ (n−1)=95−2⋅ (48−1)=1

Our quadratic equation calculator calculates it.

n=n1=48

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




Tips to related online calculators
Looking for help with calculating roots of a quadratic equation?
Do you have a system of equations and looking for calculator system of linear equations?

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: ?
  • Linsys2
    linear_eq_3 Solve two equations with two unknowns: 400x+120y=147.2 350x+200y=144
  • 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
  • What is 9
    seq What is the 15th term; x1=1.5, d=4.5?
  • Legs
    rak Cancer has 5 pairs of legs. The insect has 6 legs. 60 animals have a total of 500 legs. How much more are cancers than insects?
  • Three unknowns
    matrix_1 Solve the system of linear equations with three unknowns: A + B + C = 14 B - A - C = 4 2A - B + C = 0
  • Elimination method
    rovnice_1 Solve system of linear equations by elimination method: 5/2x + 3/5y= 4/15 1/2x + 2/5y= 2/15
  • Three workshops
    workers_24 There are 2743 people working in three workshops. In the second workshop works 140 people more than in the first and in third works 4.2 times more than the second one. How many people work in each workshop?
  • Sequence 3
    75 Write the first 5 members of an arithmetic sequence: a4=-35, a11=-105.
  • AP - simple
    sigma_1 Determine the first nine elements of sequence if a10 = -1 and d = 4
  • Sequence
    a_sequence Write the first 7 members of an arithmetic sequence: a1=-3, d=6.
  • 10th term
    seq_sum_1 What is the 10th term of the Arithmetic Progression if x1=4 and d=5?
  • AP - basics
    ap Determine first member and differentiate of the the following sequence: a3-a5=24 a4-2a5=61
  • Sheep and cows
    sheep_4 There are only sheep and cows on the farm. Sheep is eight more than cows. The number of cows is half the number of sheep. How many animals live on the farm?
  • Sequence
    seq_1 Write the first 6 members of these sequence: a1 = 5 a2 = 7 an+2 = an+1 +2 an
  • 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.
  • Sequence 2
    seq2 Write the first 5 members of an arithmetic sequence a11=-14, d=-1