Find n-th term in the series 9, 33, 73,129 …
Given a series 9, 33, 73, 129… Find the n-th term of the series.
Input : n = 4 Output : 129 Input : n = 5 Output : 201
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The given series has a pattern which is visible after subtracting it from itself after one shift
S = 9 + 33 + 73 + 129 + … tn-1 + tn S = 9 + 33 + 73 + … tn-2 + tn-1 + tn ——————————————— 0 = 9 + (24 + 40 + 56 + ….) - tn Since 24 + 40 + 56.. series in A.P with common difference of 16, we get tn = 9 + [((n-1)/2)*(2*24 + (n-1-1)d)] On solving this we get tn = 8n2 + 1
Below is the implementation of the above approach:
Time complexity: O(1)
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