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    Recurrence relations, compound interest, polynomials, number of combinations, & iteration

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    Please help with the following discrete math involving recurrence relations, compound interest, polynomials, number of combinations and iteration.

    14. Individual membership fees at the evergreen tennis club were $50 in 1970 and have increased by $2 per year since then. Write a recurrence relation and initial conditions for the membership fee n years after 1970

    2. Prove by mathematical induction that 4(2n) +3 is a solution to the recurrence relation sn = 2sn-1 -3 for n ≥ 1 with the initial condition s0 = 7

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    https://brainmass.com/math/recurrence-relation/recurrence-relations-compound-interest-polynomials-339106

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    Discrete Math: Recurrence relations, compound interest, polynomials, number of combinations, & iteration

    14. Individual membership fees at the evergreen tennis club were $50 in 1970 and have increased by $2 per year since then. Write a recurrence relation and initial conditions for the membership fee n years after 1970

    For one year, $50+$2
    For two years $50+$4
    For three years $50+$6
    For four years $50+$8
    Forwarding like this, we can see that fee for n years after 1970, is given by =$50+$2n
    2. Prove by mathematical induction that 4(2n) +3 is a solution to the recurrence relation sn = 2sn-1 -3 for n ≥ 1 with the initial condition s0 = 7
    We have sn =4(2n) +3, sn-1 =4(2n-1) +3
    So, 2sn-1 -3=2[4(2n-1) +3]-3=4(2.2n-1) +3=4(2n) +3= sn.
    So, sn=4(2n) +3, with s0=4+3=7 is the solution for the recurrence relation

    Alternate method
    Given that sn = 2sn-1 -3
    Put fn = sn-1 -3. This means s0 = 7 implies f1 = s0 -3=4.
    Hence the given relation can be written as sn-3 = 2sn-1 -6=2(sn-1 -3)
    This implies fn =2fn-1
    Clearly f1, f2, f3 ...form a G.P. with first term 4 and common ratio 2. So, fn =4.2n-1
    Hence we have fn+1 = sn -3=4.2n.
    This gives sn =4.2n+3

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 9:03 pm ad1c9bdddf>
    https://brainmass.com/math/recurrence-relation/recurrence-relations-compound-interest-polynomials-339106

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