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Math Help - recursion patterns, arithmetic/geometric equations, and sigma notations

  1. #1
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    recursion patterns, arithmetic/geometric equations, and sigma notations

    Could a kind soul please be so kind to explain what exactly the variables in the equations of arithmetic/geometric sequences mean? I would understand it so much more if i knew what u (sub N) or a meant. I have no notes Furthermore I do not quite grasp the concept of the sigma notation for my teacher is insane. Feel free to delve into that

    Thank you
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  2. #2
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    Quote Originally Posted by sodumb:( View Post
    Could a kind soul please be so kind to explain what exactly the variables in the equations of arithmetic/geometric sequences mean? I would understand it so much more if i knew what u (sub N) or a meant. I have no notes Furthermore I do not quite grasp the concept of the sigma notation for my teacher is insane. Feel free to delve into that

    Thank you
    U_n = nth term of a sequence

    U_1 = a = first terms of a sequence

    n = number of terms in a sequence or a specific term

    Arithmetic Sequences


    d = common difference ( U_n - U_{n-1} = U_{n-1}-U_{n-2} =d)

    nth term: U_n = a+(n-1)d

    Sum of n terms: S_n=\frac{n}{2}(2a + (n-1)d)


    Geometric Sequence

    r = common ratio ( \frac{U_n}{U_{n-1}} = \frac{U_{n-1}}{U_{n-2}} = r)

    nth term: U_n = ar^{n-1}

    sum to n terms ( |r| \geq 1): S_n = \frac{a(1-r^n)}{r^n} = \frac{a(r^n-1)}{r^n}

    Sum to infinity ( |r| < 1): S_{\infty} = \frac{a}{1-r}
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