Sopantyadvayamantyam
The ultimate and twice the penultimate (so · pan · tya · dva · ya · man · tyam)
What it means
In plain English: the last term, and twice the second-to-last term. Spot the rule behind a sequence of numbers, when each new number is built from the previous one — so you can predict the next number without writing them all out.
Worked example
Sequence: 3, 7, 15, 31, 63, ? Look at how each number relates to the one before. 7 = 2 × 3 + 1. 15 = 2 × 7 + 1. 31 = 2 × 15 + 1. 63 = 2 × 31 + 1. The rule: double the previous, add 1. Next term = 2 × 63 + 1 = 127.