SELECT THE NEXT NUMBER INTHE SERIES 7 11 19 35?

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  • 1 month ago

    The next number of this series is 67.

  • sepia
    Lv 7
    1 month ago

    7, 11, 19, 35, ...

    a_n = 2^(n + 1) + 3 

    7, 11, 19, 35, 67

  • Phil
    Lv 6
    1 month ago

    double the last number and minus 3.

    so the next number is 2 times 35 which is 70.

    and then minus 3 which gives you 67.

  • t[n + 1] = 2 * t[n] - 3

    From what we can see, this pattern holds true

    t[1] = 7

    t[2] = 2 * t[1] - 3 = 2 * 7 - 3 = 14 - 3 = 11

    t[3] = 2 * t[2] - 3 = 2 * 11 - 3 = 22 - 3 = 19

    t[4] = 2 * t[3] - 3 = 2 * 19 - 3 = 38 - 3 = 35

    t[5] = 2 * t[4] - 3 = 2 * 35 - 3 = 70 - 3 = 67

    t[3] = 2 * t[2] - 3 = 2 * (2 * t[1] - 3) - 3 = 4 * t[1] - 6 - 3 = 4 * t[1] - 9

    t[4] = 2 * t[3] - 3 = 2 * (4 * t[1] - 9) - 3 = 8 * t[1] - 18 - 3 = 8 * t[1] - 21

    t[5] = 2 * t[4] - 3 = 2 * (8 * t[1] - 21) - 3 = 16 * t[1] - 42 - 3 = 16 * t[1] - 45

    t[1] = 7

    t[2] = 2 * t[1] - 3 = 2^1 * t[1] - 3 * 1 = 2^1 * t[1] - 3 * (2^1 - 1)

    t[3] = 4 * t[1] - 9 = 2^2 * t[1] - 3 * 3 = 2^2 * t[1] - 3 * (2^2 - 1)

    t[4] = 8 * t[1] - 21 = 2^3 * t[1] - 3 * 7 = 2^3 * t[1] - 3 * (2^3 - 1)

    t[5] = 16 * t[1] - 45 = 2^4 * t[1] - 3 * 15 = 2^4 * t[1] - 3 * (2^4 - 1)

    t[n] = 2^(n - 1) * t[1] - 3 * (2^(n - 1) - 1)

    t[n] = 2^(n - 1) * 7 - 3 * 2^(n - 1) + 3

    t[n] = 2^(n - 1) * (7 - 3) + 3

    t[n] = 2^(n - 1) * 4 + 3

    t[n] = 2^(n + 1) + 3

    t[1] = 2^(1 + 1) + 3 = 2^2 + 3 = 4 + 3 = 7

    t[2] = 2^(2 + 1) + 3 = 2^3 + 3 = 8 + 3 = 11

    t[3] = 2^(3 + 1) + 3 = 2^4 + 3 = 16 + 3 = 19

    t[4] = 2^(4 + 1) + 3 = 2^5 + 3 = 32 + 3 = 35

    t[5] = 2^(5 + 1) + 3 = 2^6 + 3 = 64 + 3 = 67

    Seems to work.  Now you can find any term in the series, if you want.

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  • D g
    Lv 7
    1 month ago

    7 to 11 4

    11 to 19 8

    19 to 35 is 16 difference

    32 from 35 is 67

  • 1 month ago

    The nth term of that sequence could be:

    (2/3)n^3 - 2n^2 + (16/3)n + 3

    In that case:

    Term 5 is 63

  • 1 month ago

    07 ==> + 2² 

    11 ==> + 2³

    19 ==> + 2⁴ 

    35 ==> + 2⁵

    5 + ( ∑ 2^i from i = 1 to n ) 

    but  ( ∑ 2^i from i = 1 to n )  is a geometric series

    common ratio, r = 2, first term a₁ = 2

    sum of terms = a₁( rⁿ - 1 ) / ( r - 1 ) = 2( 2ⁿ - 1 ) 

    ∴ 

    5 + ( ∑ 2^i from i = 1 to n ) 

    = 5 + 2( 2ⁿ - 1 )

    for n = 5

    = 5 + 2( 2ⁿ - 1 )

    = 5 + 2( 2⁵ - 1 )

    = 67

  • Pearl
    Lv 7
    1 month ago

    i think it might be 70

  • ted s
    Lv 7
    1 month ago

    when people in math make an ASSUMPTION it is stated , you did not, so any number could be the next number for the given sequence.....{ 7 , 11, 19 , 35 , 39 , 47, 63 , 67 , 75 , 91...etc } has a pattern of adding 4  , then 8 , then 16

  • david
    Lv 7
    1 month ago

    7  ...  11 ... 19 ...  35

      7 + 4 = 11

      11 + 8 =  19

      19 + 16 = 35

       35 + 32  =  67  <<<  next term is 67

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