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Math Help - Explain/ Triangular Sequence

  1. #1
    Member GAdams's Avatar
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    Explain/ Triangular Sequence

    Can anybody help me with these two questions:

    1. Given a triangle with the 'base' at the bottom, single angle at the top. The base line is extended to the right. The exterior angle is 90 + (x/2). The top angle is x. How do I prove that it is isosceles?

    2. Explain why the (n+1)th term of a triangular sequence is given by
    1/2(n+1)(n+2) given that the nth term is 1/2n(n+1)
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  2. #2
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    1. Given a triangle with the 'base' at the bottom, single angle at the top. The base line is extended to the right. The exterior angle is 90 + (x/2). The top angle is x. How do I prove that it is isosceles?
    interior angle adjacent to the given exterior angle is 180 - \left(90 + \frac{x}{2}\right) = 90 - \frac{x}{2}

    remaining base angle is 180 - \left[x + \left(90 - \frac{x}{2}\right)\right]

    simplify this expression and see what you get.


    2. Explain why the (n+1)th term of a triangular sequence is given by 1/2(n+1)(n+2) given that the nth term is 1/2n(n+1)
    nth term is \frac{n(n+1)}{2} ... so, (n+1)st term is formed by replacing n with n+1 ... \frac{(n+1)[(n+1)+1]}{2}

    simplify the last expression.
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