Problem 6 [15 pts]: Plushies Always Collect Lucia has often borrowed from the Plushie Group to continue growing her plushie collection. She now has a large debt of hugs to pay off. The Plushie group never offers the interest rates on what she borrows, but always communicates them as projections over the next few weeks. i. ii. The head of the Plushie Group has offered a new way of paying off what she owes. They tell Lucia how many hugs she must give each week. In the rst week, she must give 4 hugs. In the second week, she must give 23 hugs. In the third week, she must give 62 hugs. In the fourth week, 121 hugs. In the fth week, 200 hugs. If she must continue in this pattern, after 10 weeks, how many hugs will she have given in total across all 10 weeks? Show all of the work, including any work for nding the sequence and solving any series. You will need the following property: i .2 = n(n+ 1)(2n+ 1) 5:1 6 Having paid off the hugs, Lucia asks to borrow for some more plushies, particularly the large reversible octopi}. She is given two options for borrowing 0 She can borrow for 1000 hugs. On week 1, she will still owe the 1000 hugs. On week 2, the debt becomes 1350 hugs total. On week 3, it becomes 1822.5 hugs. On week 4, it becomes 2460.38 hugs. On week 5, it becomes 3321.51 hugs. 0 She can borrow for 10000 hugs. On week 1, she will still owe the 10000 hugs. On week 2, the debt becomes 10050 hugs total. On week 3, it becomes 10100.2 hugs. On week 4, it becomes 10150.8 hugs. On week 5, it becomes 10201.5 hugs. Assume fractional hugs can be fullled with awkward hugs. Which option will have her owe more hugs on week 10? Show your work and reasoning. In particular, you must use the sequence and series tools we have learned in this course instead of the principal and interest rate formula