Welcome to Episode 7 of Season 1: Unlocking Number Theory and Algebra! This episode presents mathematical problems and solutions focusing on arithmetic, geometric, and arithmetic-geometric sequences. Key concepts covered include relevant formulas, such as the sum of arithmetic and geometric series. Examples illustrate problem-solving techniques using these formulas within the context of the American Invitational Mathematics Examination (AIME). Additional topics explored are Vieta's Theorem and its application to polynomials. The text ultimately aims to equip readers with the skills needed to solve advanced mathematical problems involving sequences and polynomials.