1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Sergeu [11.5K]
3 years ago
9

What's the next number? 0 , 1/3 , 1/2 , 3/5 , 2/3​

Mathematics
1 answer:
madam [21]3 years ago
6 0

Answer:

The next number of the series 0, 1/3, 1/2, 3/5, and 2/3 is 5/7

Step-by-step explanation:

The given numbers are;

0, 1/3, 1/2, 3/5, and 2/3

The number sequence is formed adding \dfrac{1}{\left (\dfrac{n^2 + n}{2} \right ) } to each (n - 1)th term to get the nth term number in the sequence, with the first term equal to 0, as follows;

For the 2nd term, the (n - 1)th term is 0, and n = 2, gives;

The

0 +\dfrac{1}{\left (\dfrac{2^2 + 2}{2} \right ) } = 0 + \dfrac{1}{3} = \dfrac{1}{3}

For the 3rd term, the (n - 1)th term is 1/3, and n = 3, gives;

\dfrac{1}{3} +\dfrac{1}{\left (\dfrac{3^2 + 3}{2} \right ) } = \dfrac{1}{3} + \dfrac{1}{6} = \dfrac{1}{2}

For the 4th term, the (n - 1)th term is 1/2, and n = 4, gives;

\dfrac{1}{2} +\dfrac{1}{\left (\dfrac{4^2 + 4}{2} \right ) } = \dfrac{1}{2} + \dfrac{1}{10} = \dfrac{3}{5}

For the 5th term, the (n - 1)th term is 3/5, and n = 5, gives;

\dfrac{3}{5} +\dfrac{1}{\left (\dfrac{5^2 + 5}{2} \right ) } = \dfrac{3}{5} + \dfrac{1}{15} = \dfrac{2}{3}

For the next or 6th term, the (n - 1)th term is 2/3, and n = 6, gives;

\dfrac{2}{3} +\dfrac{1}{\left (\dfrac{6^2 + 6}{2} \right ) } = \dfrac{2}{3} + \dfrac{1}{21} =  \dfrac{15}{21} = \dfrac{5}{7}

The next number of the series 0, 1/3, 1/2, 3/5, and 2/3 = 5/7.

You might be interested in
Find the value of x. <br> A. x= 1 <br> B. x=5 <br> C. x=19 <br> D. x=37
Strike441 [17]
Triangle WYZ and triangle TWY are congruent, therefore WZ = TW
WZ = TW
3x - 5 = 2x
3x - 2x = 5
x = 5

The value of x is 5
6 0
3 years ago
Read 2 more answers
Solve the system of equations by graphing. If the system has no solution or infinitely many so state.
S_A_V [24]
The systems will intersect at (1,-4), and i think the system has infinite solutions (not sure)
6 0
3 years ago
Area= 169(pie)mm(squared)<br><br> What's the radius and diameter
Natali [406]

You would have to divide by 3.14 to find the radius squared, and to find the diameter, just add the radius plus the radius.
4 0
3 years ago
A-2.5<br> 2a-22.7<br> a+1.3<br> 21.5<br> What’s a
rewona [7]

Answer:

2.4

Step-by-step explanation:

8 0
3 years ago
Can someone help me please
NikAS [45]
Justin rides 550 kilometers
or
justin rides 17 meter
6 0
3 years ago
Other questions:
  • Axis of symmetry for f(x) = -2x2 + 20x -42
    15·2 answers
  • You are purchasing carpeting for an office building. The space to be carpeted is 30 feet by 50 feet. Company A charges $2.99 per
    12·1 answer
  • State the name of the property.<br> (24+9)+4=24+(9+4).
    11·2 answers
  • In the year 1990, a total of 320 points were scored in a basketball game between the golden state warriors and the Denver nugget
    14·1 answer
  • 17. What is 43 in expanded form?
    14·2 answers
  • Solve for p, I don't know what else to add but yeah<br> solve for p?<br> Also explain
    5·1 answer
  • PONTOS GRATIS BRASIL ​
    10·2 answers
  • A PAIR OF JEANS MARKED AT R450 IS SOLD AT DISCOUNT OF 25%.​
    8·1 answer
  • Please help and explain.
    8·2 answers
  • Find the values of P for which the quadratic equation 4x²+px+3=0?​
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!