{"type":"video","version":"1.0","html":"<iframe src=\"https://www.loom.com/embed/430131e79c98402097fff9bd1a1bf91c\" frameborder=\"0\" width=\"1266\" height=\"949\" webkitallowfullscreen mozallowfullscreen allowfullscreen></iframe>","height":949,"width":1266,"provider_name":"Loom","provider_url":"https://www.loom.com","thumbnail_height":949,"thumbnail_width":1266,"thumbnail_url":"https://cdn.loom.com/sessions/thumbnails/430131e79c98402097fff9bd1a1bf91c-b267fda8dc46ae0b.gif","duration":2173.88,"title":"9MA0 Pure Set 6A Sequences &amp; Series - Arithmetic &amp; Recurrence Relations","description":"In 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."}