The pattern 5, 11, 21, 35, … is given by the rule tn = 2n2 + 3.Show that the difference between consecutive terms, starting at the nth, is 4n + 2
Question
Solution 1
Sure, let's break it down:
The nth term of the sequence is given by the formula tn = 2n^2 + 3.
The (n+1)th term of the sequence is given by the formula t(n+1) = 2(n+1)^2 + 3.
The difference between consecutive terms starting at the nth term is given by:
t(n+1) - tn = [2(n+1)^2 + 3] - [2n^2 + 3]
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