math

write triangular formulas to find numbers between 10 and 30

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  1. If you think about triangular numbers then:

    xn = n ( n + 1 ) / 2

    n = 1

    x1 = 1 * ( 1 + 1 ) / 2 =

    1 * 2 / 2 = 2 / 2 = 1

    1 is less than 10.

    n = 2

    x2 = 2 * ( 2 + 1 ) / 2 =

    2 * 3 / 2 = 6 / 2 = 3

    3 is less than 10.

    n = 3

    x3 = 3 * ( 3 + 1 ) / 2 =

    3 * 4 / 2 = 12 / 2 = 6

    6 is less than 10.

    n = 4

    x4 = 4 * ( 4 + 1 ) / 2 =

    4 * 5 / 2 = 20 / 2 = 10

    n = 5

    x5 = 5 * ( 5 + 1 ) / 2 =

    5 * 6 / 2 = 30 / 2 = 15

    n = 6

    x6 = 6 * ( 6 + 1 ) / 2 =

    6 * 7 / 2 = 42 / 2 = 21

    n = 7

    x7 = 7 * ( 7 + 1 ) / 2 =

    7 * 8 / 2 = 56 / 2 = 28

    n = 8

    x8 = 8 * ( 9 + 1 ) / 2 =

    8 * 9 / 2 = 72 / 2 = 36

    36 is greater then 30.

    So a triangular numbers between 10 and 30:

    10 , 15 , 21 , 28

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