Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

the third and fourth terms of an arithmetic sequence are -3 and 0.?

how do i found the 1000th term

9 Answers

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  • Since you're dealing with an AP(arithmetric sequence), let the nth term be Tn

    Generally, Tn=a+(n-1)d

    Where a=first term; n=number of terms; d=common difference

    From the first point, 3rd term=-3 and from the second point, 4th term=0

    This means, 

    T3=a+(3-1)d=-3

    a+2d=-3..................1

    Also, T4=a+(4-1)d=0

    a+3d=0

    a=-3d.......................2

    Substitute a as -3d into equation 1;

    -3d+2d=-3

    -d=-3

    d=3

    Also, from equation 2, a=-3(3)=-9

    Hence, a=-9, d=3

    Tn=-9+(n-1)3

    Tn=-9+3n-3=3n-12

    Tn=3n-12

    Finally, when n=1000

    T1000=3(1000)-12

              =3000-12

              =2988

    Hence, 1000th term is 2988  

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  • 1 month ago

    -9, -6, -3, 0, ...

    -9, -6, -3, 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, ...

    a_n = 3 (n - 4) 

    The 1000th term is 2988

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  • nbsale
    Lv 6
    1 month ago

    I think of the difference as a "step."

    -3 to 0 means it increases in steps of 3

    You have the 4th term, which is 0.

    You want the 1000th term which is 996 steps away.

    So just add 996 step to the 4th term.

    0 + 3*996 = 2988 is the 1000th term

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  • sepia
    Lv 7
    1 month ago

     The third and fourth terms of an arithmetic sequence are -3 and 0.

     -9, -6, -3, 0, ...

     a_n = 3 (n - 4) 

     The 1000th term is 3(996) = 2988.

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  • 1 month ago

    Common difference is 3

    Hence, 2nd term is -6 and 1st term is -9

    nth term is -9 + 3(n - 1)

    i.e. 3n - 12

    so, 1000th term is 3(1000) - 12 => 2988

    :)>

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  • 1 month ago

    For an arithmetic sequence:

    a₁

    a₂ = a₁ + d ← where d is the common difference, i.e.: 5

    a₃ = a₂ + d = a₁ + 2d = - 3

    a₄ = a₃ + d = a₁ + 3d = 0

    You can obtain a system with 2 equations:

    (1) : a₁ + 2d = - 3

    (2) : a₁ + 3d = 0

    Then you calculate (1) - (2):

    (a₁ + 2d) - (a₁ + 3d) = - 3 - 0

    a₁ + 2d - a₁ - 3d = - 3

    d = 3

    Recall a₃ = a₁ + 2d = - 3

    a₁ + 2d = - 3

    a₁ = - 3 - 2d → we've just seen that: d = 3

    a₁ = - 9

    Recall:

    a₁

    a₂ = a₁ + d

    a₃ = a₁ + 2d

    a₄ = a₁ + 3d

    …and you can generalize writing:

    a(n) = a₁ + (n - 1).d → for the 1000th term, n = 1000

    a₁₀₀₀ = - 9 + (1000 - 1).3

    a₁₀₀₀ = - 9 + (999 * 3)

    a₁₀₀₀ = 2988

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  • 1 month ago

    nth term of an Arithmetic Sequence is given by -

    T(n)  = First term (suppose-a) + ( n-1 ) (common difference ( say d )

    Hence ---

    T(3) = a + ( 3 - 1 ) d   =  - 3

    => a + 2 d  =  - 3  .................... (1)   Similarly --

    T(4) =  a + ( 4 - 1 ) d  =  0

    => a + 3 d  =  0  ............. (2)

    from (1) and (2) we get 

    a  =  - 9  and d  =  3

    Hence  T(1000)  =  - 9 + ( 1000 - 1 ) 3  =  3000 - 12  =  2988.......Answer

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  • Anonymous
    1 month ago

    Difference is 3.

    2nd tem is -6

    1st term is -9

    n-t term is a + (n-1)d

    1000th term = -9 + (1000-1)3 = 2988

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  • 1 month ago

    if -3 and 0 are third or fourth terms,it mean it is increasing by 3, so if we start from 0 we have 996 terms left to get to 1000 terms.

    so the 1000th term is the term x how much it is increasing

    we have 996 terms if we start from 0

    996 x 3

    =2988

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