recurrence realtionship questions
- Thread starter fatima_q
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A recurrence relation is an equation that recursively defines a sequence of values, whereby
each element of a sequence can be written as a function of preceding element(s); the first element of the sequence will be uniquely defined by an initial value of the recurrence relation.
Specifically, if a sequence un can be expressed as a function of only n and the immediate preceding element un−1, i.e., un = g(n,un−1), then we say that un is a recurrence relation of order 1. The values of the entire sequence can be calculated recursively starting from the initial value say u1 and then by u2 = g(2,u1) and more generally un = g(n,un−1) for n = 3,4,5,···.
(a) Write down a recurrence relation for ¨ an. Explain your thought process in words (e.g., using the timeline approach) OR prove the result mathematically by first principles. Also write down the initial value for the sequence.
(b) Given an effective discrete periodic rate of 3% per period, tabulate the values of ¨ an for n = 1,2,··· ,30
each element of a sequence can be written as a function of preceding element(s); the first element of the sequence will be uniquely defined by an initial value of the recurrence relation.
Specifically, if a sequence un can be expressed as a function of only n and the immediate preceding element un−1, i.e., un = g(n,un−1), then we say that un is a recurrence relation of order 1. The values of the entire sequence can be calculated recursively starting from the initial value say u1 and then by u2 = g(2,u1) and more generally un = g(n,un−1) for n = 3,4,5,···.
(a) Write down a recurrence relation for ¨ an. Explain your thought process in words (e.g., using the timeline approach) OR prove the result mathematically by first principles. Also write down the initial value for the sequence.
(b) Given an effective discrete periodic rate of 3% per period, tabulate the values of ¨ an for n = 1,2,··· ,30