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The paper demonstrates a way how to find a formula for the nth term of a sequence that is given recursively. We concentrate only on a special case when the sequence is given by a linear recurrence relations of the first order with constant coefficients. There are given two applications of the derived formula at the end of the paper. Particularly we formulate and solve a problem of mortgage of loans and a problem of Towers of Benares which is also known as a problem of Towers of Hanoi.
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