# Perpetuity

This crossword clue is for the definition: Perpetuity.
it’s A 10 letters crossword puzzle definition.
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Last seen on: The Sun – Two Speed Crossword – Oct 16 2020

### Random information on the term “Perpetuity”:

In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-one number called the common ratio. For example, the sequence 2, 6, 18, 54, … is a geometric progression with common ratio 3. Similarly 10, 5, 2.5, 1.25, … is a geometric sequence with common ratio 1/2.

Examples of a geometric sequence are powers rk of a fixed number r, such as 2k and 3k. The general form of a geometric sequence is

where r ≠ 1 is the common ratio and a is a scale factor, equal to the sequence’s start value.

The n-th term of a geometric sequence with initial value a = a0 and common ratio r is given by

Such a geometric sequence also follows the recursive relation

Generally, to check whether a given sequence is geometric, one simply checks whether successive entries in the sequence all have the same ratio.

The common ratio of a geometric sequence may be negative, resulting in an alternating sequence, with numbers alternating between positive and negative. For instance