Iteration: I1 Again and againYou are going to investigate sequences of numbers produced by a term to term rule. This rule tells you how to get from any term in the sequence to the next one.You can vary the values of A and B. You can also choose the first number. The spreadsheet will work out the first 20 numbers in the sequence.
(a) Make A = 2 and B = 1.
What happens to the sequence of values? You should see that the values creep closer and closer towards a particular number. This means the sequence is converging.
(b) What other values of A and B make the sequence converge?
(c) Can you find a connection between your values of A and B and the number that the sequence is converging towards? This number is called the limit.
(d) If the sequence does not creep towards a limit but instead gets larger and larger, we say the sequence is diverging. What values of A and B make the sequence diverge?
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