Cadent house

In Jyotisha 12 signs of the horoscope are divided into three segments of four quadrants 1-4-7-10 / 2-5-8-11 and 3-6-9-12. In this 1-4-7-10 are Angular houses, 2-5-8-11 are Succedent houses and 3-6-9-12 are the Cadent houses. Each quadrant starts with an angular house then there is Succedent house, and finishes with a Cadent house. Angular houses are most powerful of the three types and Succedent being somewhat less powerful and lastly the Cadent houses least powerful of the batch. There are four quadrants in an astrological chart, providing four angular houses, four Succedent houses and four Cadent houses. We can say Cadent is a term used to refer to the 3rd, 6th, 9th and 12th houses in an astrological chart.

The term “Cadent” is derived from the Latin word cado, which means “to fall down” or “to decline”  "falling, or coming to an end or resolution".  The Latin term was originally derived from the Greek word apoklima (ἀπόκλιμα), which means “slope” or “decline”. The Greeks called the Cadent houses apoklima, which also literally means "falling" or "decline," because the houses were seen to be falling away from the strength of the angular houses, which were considered to be most influential because of their perpendicular and oppositive relationships to the Ascendant.
The word apoklima also carries a denotation of degeneration and decline. Our English word "cadent" comes from the Latin translation of apoklima and is the source of our word "cadet," which originally meant a lesser branch of the family, or the younger son.
The keyword for cadent is "dispersal". One meaning of dispersal is "giving out". When a group of people separate and go their separate ways, we say they disperse. Another way to express this is in terms of reflection (thinking) and consequences. Having taken action as some being, we gain security, or gather together values and having succeeded (or not) we reflect upon (think seriously about) the cycle of action and deal with the consequences.
In the cadent houses, we think about what has gone before and what we will do, or what will happen in the future. Here we do our thinking before we take the next action. In the world, the cadent houses come at a time when the seasons are changing from one to the other. In the natal chart we think about the past and the future in a more or less critical, detailed and impersonal fashion, with the intention of using what we have learned to take our next steps in life.

The Cadent houses (third, sixth, ninth, and twelfth houses) are ruled by mutable signs: Gemini, Virgo, Sagittarius, and Pisces.

 The third house of the horoscope governs our siblings, letters and messengers, our neighborhood, perception, learning and short trips. Modern astrologers have also connected it our ability to communicate in short our communication skills and to intellectualize.The third house is concerned with communication, which in one sense could mean we disperse our knowledge and experience to others.
The sixth house of the horoscope deals primarily individual performance, this can be both at his or her job or simply how he or she performs a job at home. It also deals with diet and health of an individual, and also to our duties and responsibilities, and the most routine aspects of work. The sixth is the house of servants, and so may also refer to our service to others, but also to slavery, or that which we are obliged to do but do not necessarily want to do. It has been connected by Lilly to smaller domestic animals as well, "and the profit and loss got thereby."The sixth house is the House Of Service, where we willingly give our personal resources and skills to help others 
The ninth house is the opposite of the third house. The ninth house of the horoscope governs our higher cognition, religious beliefs, and level of awareness. It is also the house of higher education and philosophy and is connected with long journeys far from home. Some modern astrologers also give it an association with the law. It deals with how well you understand the principles. The ninth house also signifies a person’s philosophies and spiritual beliefs. It also rules longer trips that require overnight stay

The twelfth house of the horoscope governs troubles, self-undoing, secret enemies, and imprisonment (for example in asylums or penitentiaries), as well as larger domestic animals, such as draught animals. The twelfth house deals with the unpleasant – our problems, undisclosed enemies, and secrets that can ruin the individual. Some astrologers connect this house to incidents from past lives, i.e. karma.