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koli123able

  • 3 years ago

The sum of first 14 terms of 1,1.4,1.8,.... is equal to the sum of first n terms of 5.6,5.8,6.0,.... , find the value of n

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  1. sauravshakya
    • 3 years ago
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    1,1.4,1.8,.... This is in AP with first term 1 and common difference 0.4

  2. sauravshakya
    • 3 years ago
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    Use sum formula of AP

  3. amoodarya
    • 3 years ago
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    14/2(a1+a14)=n/2(5.6+5.6+(n-1)*0.2)

  4. amoodarya
    • 3 years ago
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    14/2(1+1+13(.4))=n/2(5.6+5.6+(n-1)*0.2)

  5. koli123able
    • 3 years ago
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    i did the first A.P and its coming 50.4

  6. sauravshakya
    • 3 years ago
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    S14 =14/2 {2*1 + (14-1)0.4} = 50.4

  7. koli123able
    • 3 years ago
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    i am stuck here

  8. sauravshakya
    • 3 years ago
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    5.6,5.8,6.0,.... This is in AP with common difference 0.2 andfirt term 5.6

  9. koli123able
    • 3 years ago
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    \[50.4=\frac{ n }{ 2 }[(2*5.6)+(n-1)*0.2]\]

  10. koli123able
    • 3 years ago
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    stuck here

  11. sauravshakya
    • 3 years ago
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    Sn=50.4 n/2 { 2*5.6 + (n-1)0.2}=50.4 n{11 - 0.2n}=100.8

  12. koli123able
    • 3 years ago
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    2*5.6 its 11.2

  13. sauravshakya
    • 3 years ago
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    11n -0.2n^2 =100.8 11n -2/10 n^2 =100.8 110n -2n^2 =1008

  14. sauravshakya
    • 3 years ago
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    11.2-0.2=11

  15. koli123able
    • 3 years ago
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    oh

  16. sauravshakya
    • 3 years ago
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    110n -2n^2 =1008 2n^2-110n+1008=0 n^2-55n+504=0

  17. koli123able
    • 3 years ago
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    how did became 110n -2n^2 =1008

  18. sauravshakya
    • 3 years ago
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    |dw:1359028396466:dw|

  19. koli123able
    • 3 years ago
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    ok

  20. sauravshakya
    • 3 years ago
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    Now,n^2-55n+504=0 CAN u solve for n

  21. koli123able
    • 3 years ago
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    n= -11.61 and n= -43.38

  22. koli123able
    • 3 years ago
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    now what?

  23. koli123able
    • 3 years ago
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    The Answer should come n=8...i checked the answers

  24. sauravshakya
    • 3 years ago
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    n=8 is surely not the correct solution

  25. koli123able
    • 3 years ago
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    the book says that answer is n=8

  26. koli123able
    • 3 years ago
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    how will it come 8

  27. sauravshakya
    • 3 years ago
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    Sorry I did a algebra mistake

  28. sauravshakya
    • 3 years ago
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    n=8 is correct

  29. koli123able
    • 3 years ago
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    how????? plz plz tell me

  30. sauravshakya
    • 3 years ago
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    Sn=50.4 n/2 { 2*5.6 + (n-1)0.2}=50.4 n/2 {11+0.2n}=50.4 n{11+0.2n}=100.8 11n+0,2n^2=100.8 11n +2/10 n^2 =100.8 110n+2n^2=1008 55n+n^2=504 n^2+55n-504=0 n^2+(63-8)n-504=0 n^2 +63n -8n-504=0 n(n+63)-8(n+63)=0 (n-8)(n+63)=0

  31. sauravshakya
    • 3 years ago
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    Now, either n-8=0 n=8 OR n+63=0 n=-63 BUT n cannot be negative So, n=8

  32. sauravshakya
    • 3 years ago
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    got it?

  33. koli123able
    • 3 years ago
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    thanks

  34. sauravshakya
    • 3 years ago
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    welcome

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