What is the general term of 1,2,4,7,11,16,22?

1. 51

   michaelneLaposted 14 years ago

   What is the general term of 1,2,4,7,11,16,22?
   
   Is there any technique how to find the general term? plsss help me.

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   1. 60

      Taiwo Oluwaseyeposted 7 years agoin reply to this

      Addition of 1 2 3 4 5 6 7......
      1+1=2
      2+2=4
      3+4=7
      4+7=11
      5+11=16
      and so on

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      1. 60

         Taiwo Oluwaseyeposted 7 years agoin reply to this

         6+16=22

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   2. 59

      kkapkaaposted 6 years agoin reply to this

      Fibonacci Sequence

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      1. 58

         antbytesposted 4 years agoin reply to this

         The Fibonacci Sequence is the series of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ... The next number is found by adding up the two numbers before it.

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      2. 59

         learningradiusposted 4 years agoin reply to this

         It is not fibonacci series. Fibonacci series is like 0,1,1,2,3,5,8,13...... (adding adjacent number).
         The peculiarity of the question raised ( general term 1,2,4,7,11,16,22). Adding natural number to each of the terms in the series, we get the result.
         
         For people looking for UPSC Free Mock Test, visit https://learningradius.com/

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2. 60

   L.C. Smithposted 14 years ago

   I'm not sure if this is a mathematical question, but it looks like you have posted a series of numbers that flow in the following way:
   1+1 = 2
   2+2 = 4
   4+3 = 7
   7+4 = 11
   11+5 = 16
   16+6 = 22
   
   1 was added to the 1st number to get 2, that sum, 2, was added to 2, because it was the second number, to get 4.  The sum of 4 was added to 3, because it was the third number, to get 7.  Yada, yada, yada...

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   1. 60

      GoldyIndianposted 9 years agoin reply to this

      I got suitable formulea for nth term and sum this type sequence and more sequence
      1+2+4+7+11+16+22.......

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3. 51

   michaelneLaposted 14 years ago

   yah, but what is the exact formula to come up with this kind of problem.. thank you for your answer. ^^

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4. 52

   mathman32503posted 14 years ago

   To find the nth term of the sequence:
   
   0.5*n^2 - 0.5*n + 1
   
   If we look at the difference between successive terms, we see that the differences are not the same - so a linear function will not work.
   
   1  2  3  4  5  6   
   
   But if we look at the difference between successive differences (second-order differences, if you will), we see that these are the same - so a quadratic function will work.
   
   1  1  1  1  1  1     
   
   To find the function, I looked for some pattern.  I listed the triangular numbers (1 3 6 10 15 21 27); the nth triangular number is the sum of the positive integers less than or equal to n.  It appears as though the nth term of the sequence is adjusted down (by differing amounts) from the triangular number.  Specifically, to find the nth term, we subtract (n-1) from the nth triangular number. 
   
   This yields:
   
   (Sum of numbers 1 through n) - (n-1)
   
   = 0.5(n)(n+1) - n + 1               
   
   = 0.5*n^2 + 0.5*n - n + 1         
   
   = 0.5*n^2 - 0.5*n + 1
   
   I know that I've merely given you my thought process rather than a hard, fast method to be applied every time.  All I can say is that finding the nth term is like solving any other problem type: you get better with experience.  You build an intuition. 
   
   I hope this helps.

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   1. 60

      GoldyIndianposted 9 years agoin reply to this

      This is formula regarding to error method

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5. 60

   GoldyIndianposted 11 years ago

   I have exact formulae
   But first I will regist it
   1+2+4+7+11+16+........
   Cool my all Maths expert

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6. 81

   gmwilliamsposted 10 years ago

   
   
   I would call this a sequential equation e.g. 1,2,4,7,11,16,22, 29.  You see:
   1+1=2
   2+2=4
   4+3=7
   7+4=11
   11+5=16
   16+6=22
   22+7=29.....and 29+8=37, 37+9=46, the main component is adding sequential numbers to the equation.

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7. 69

   androidfanposted 9 years ago

   The simple formula of this number series is like that:-
   
   1st Digit + 1= 2nd Digit,
   2nd Digit + 2= 3rd Digit.
   3rd digit + 3= 4th Digit.
   
   So, Nth Digit = (N-1)th Digit + (N-1): It is the formula.
   
   So, if n=5, then the 5th Digit = (5-1)th Digit+(5-1)
                                               = 4th Digit + 4
                                               = 7+4= 11.

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   1. 60

      GoldyIndianposted 9 years agoin reply to this

      What is sum formulea Of this type sequence
      I got nth term formulea and sum formulea

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8. 60

   Soleman Aliposted 8 years ago

   1+1=2
   2+(1+1)=4
   4+(1+2)=7
   7+(1+3)=11
   11+(1+4)=16
   16+(1+5)=22
   22+(1+6)=29

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9. 61

   crowsnestposted 8 years ago

   Xn = X(n-1) + (n-1) is the formula you are looking for.
   
   Where Xn is the nth (or general) term of the sequence.
   So, X(n-1) is the term directly before Xn.
   And (n-1) is just the integral value of n minus 1.
   
   Example: n=5
   Xn = 11
   X(n-1) = 7
   n-1 = 5-1 = 4
   
   So using the formula, 11 = 7 + 4

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10. 51

    arash prkposted 7 years ago

    1+0=1   1+1=2   1+3=4    ...
    
    general rule is :
    
    (n(n-1))/2+1

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11. 60

    Taiwo Oluwaseyeposted 7 years ago

    1 2 4 7 11 16 22
    
    1st difference:  0 1 2 3 4 5 6 7.........
    
    1+0=1
    1+1=2
    2+2=4
    4+3=7
    7+4=11
    11+5=16
    16+6= 22
    22+7= 29
    
    And so .....

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12. 74

    MarieLBposted 7 years ago

    next comes 29
    Each time you add up one more than the last time.
    So  to the first no ie:  1  you add 1
    Then you add 2,3,4,5,6,7

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13. 51

    Oluwaseyetposted 7 years ago

    Yes there is a technique it is called Quadratic Sequence
    
                                                     1,2,4,7, 11, 16,22
    
    
    Difference 1 2 3 4 5 6
    0+1=1
    1+1=2
    2+2=4
    3+4=7
    4+7=11
    5+11=16
    6+16=22
    7+22=29
    8+29=37
    And so on

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14. 58

    soumya reddyposted 7 years ago

    1,2,4,7,11,16,22 next one is 29. check it once http://bit.ly/2pHf8sk

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15. 55

    Unogeeksposted 2 years ago

    next is 29 get solution here https://bit.ly/3MaYBTn

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16. 54

    paulspavanposted 2 years ago

    Communications link failure by Mulesoft 4.x only in localhost
    
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