Prove that the statements are true by mathematical induction. Show all of your work for both cases. 11 + 19 + 27 + ... + 8n + 3 = n(4n + 7)

36+324+900+...+(12n-6 = 12n(4 - 1)

Acompany manufactures three types of cabinets. it makes 110 cabinets each week. in the first week, the sum of the number of type-1 cabinets and twice the number of type-2 cabinets produced was 10 more than the number of type-3 cabinets produced. the next week, the number of type-1 cabinets produced was three times more than in the first week, no type-2 cabinets were produced, and the number of type-3 cabinets produced was the same as in the previous week.