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Math Help - Sequences (arithmetic/geometric)

  1. #1
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    Sequences (arithmetic/geometric)

    Let ak= 3^k,
    bk=5k-3 and
    ck= ak+bk
    =3^k +5k-3

    a/ which type of sequence is ak and write out a formula for the value of a1+a2+...+an.

    b/ which type of sequence is bk and write out a formula for the value of b1+b2+...+bn.

    c/ write out formula for c1+c2+...c10.


    I am very unsure about how to answer this question.. can somebody help me please?
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  2. #2
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    Quote Originally Posted by fvaras89 View Post
    Let ak= 3^k,
    bk=5k-3 and
    ck= ak+bk
    =3^k +5k-3

    a/ which type of sequence is ak and write out a formula for the value of a1+a2+...+an.

    b/ which type of sequence is bk and write out a formula for the value of b1+b2+...+bn.

    c/ write out formula for c1+c2+...c10.


    I am very unsure about how to answer this question.. can somebody help me please?

    This belongs in precalculus or prealgebra, not here. Anyway, the following are some basic definitions for you to solve your problem. If you get stuck somewhere write back, show your work and ask:

    == A sequence \{a_n\} is a geometric sequence if for any subindex k we have that \frac{a_{k+1}}{a_k}=q is the same constant number, which is then called the quotient or ratio of the geo. seq.

    == A sequence \{b_n\} is an arithmetic sequence if for any k we have that b_{k+1}-b_k=d is the same constant number d, which is then called the difference of the arit. seq.

    == The sum of the first n elements of a geo. seq. with ratio q is given by \sum\limits_{k=1}^n\,a_k=a_1\,\frac{q^{n+1}-1}{q-1}

    = The sum of the first n elements of an arit. seq. with difference d is given by \sum\limits_{k=1}^n\,b_k=\frac{n}{2}\left(2a_1+d(n-1)\right)

    Tonio
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  3. #3
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    tonio is of course correct but if you do not understand his hints then just write out the series.

    if it's a geometric series then when you divide one term by the term before it, you will get the same answer, no matter which two consecutive terms you pick.

    Likewise, if you pick two consecutive terms of an arithmetic series you will get the same answer if you subtract them.

    For part c) use the result that tonio has kindly provided. One part of the sequence you are given is arithmetic, the other, geometric. Add them
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