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30MSC 2023 #22: Sequences

30MSC 2023 #22: Sequences

A sequence is a list of numbers that usually follow a particular pattern. The pattern may be increasing, decreasing, or recurring. To know the missing terms in a sequence we have to know the rules defining the terms of the sequence.

We can see from our example, which was taken from the senior questionnaire  of IVMO 2021, ”The first five terms of a sequence are 0, 3, 8, 15, 24, … What is the 98th term?“ ,that the differences between the terms are successive odd numbers starting from 3. This suggests that the sequence is related to the squares of numbers.

We can confirm this by adding 1 to every term making the first 5 terms,  1, 4, 9, 16, 25. Therefore, we need only to find the square of 98 and subtract 1 from it to get the 98th term of the sequence.

The Vedic Sutra, “Whatever the Deficiency, Lessen by That Amount and set-up the Square of the Deficiency”, provides an easy way to find the square of 98.  Its deficiency from 100 is 2. So, 98 less two is 96 and the square of 2 is 04 (the base is 100 which has 2 zeroes, and the second part of the answer must occupy two places). 98^2 is 9604.

The 98th term of the sequence is 9604 – 1 = 9603.

Further discussion on sequences is found in Chapter 2 of our forthcoming book, 30 Master Strategies in Computing Vol III.

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