video1.0<iframe src="https://www.loom.com/embed/430131e79c98402097fff9bd1a1bf91c" frameborder="0" width="1266" height="949" webkitallowfullscreen mozallowfullscreen allowfullscreen></iframe>9491266Loomhttps://www.loom.com9491266https://cdn.loom.com/sessions/thumbnails/430131e79c98402097fff9bd1a1bf91c-b267fda8dc46ae0b.gif2173.88In this video, I walk through various questions related to arithmetic series, sequences, and recurrence relations. I start with an arithmetic series where the first term is 16 and the 21st term is 24, leading to a common difference of 0.4, and I calculate the sum of the first 500 terms to be 57,900. I also provide a proof for the sum formula and discuss a scenario involving James saving money for a printer costing £64, where I find that he needs 10 weeks to save enough. Additionally, I explore a periodic sequence and its properties, concluding with a recurrence relation that leads to specific values. Please review the calculations and proofs presented, as they may be useful for your understanding of these concepts.