Prove the Following Statement by Mathematical Induction $1+7+13+\ldots+(6 n-5)=n(3 n-2)$

question 46

Essay

Prove the following statement by mathematical induction. $1+7+13+\ldots+(6 n-5)=n(3 n-2)$

---

Definitions:

Daily Enemas

The practice of introducing liquid into the rectum and colon via the anus on a daily basis, typically to encourage bowel movements or cleanse the colon.

Antihistamines

Medications used to relieve or prevent the symptoms of allergies and colds by blocking the action of histamine in the body.

Seasonal Allergies

Allergic reactions to airborne substances such as pollen, that occur during specific seasons causing symptoms like sneezing and congestion.

Viral Illness

Illnesses caused by viruses, which are microscopic infectious agents that can lead to a wide range of diseases, from the common cold to more severe illnesses.