Find the rst six terms of the sequence. a1:l,an:an_1+8 Find an explicit rule for the nth term of the sequence. 1, 2, 4, 8, Find a recursive rule for the nth term of the sequence. -7, -42, -252, -1512, Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false. (4 points each.) 4(40 + 1)(8n + 7) 6 1.4-6+5-7+6-8+...+4n(4n+2)= 2.12+42+ 72+ + (Sn-2F: "(6\"2 4"\") 2 For the given statement Pn, write the statements P1, Pk, and Pm. (2 points) 3.2+4+6+...+2n=n(n+1) Find the sum of the first 8 terms of the sequence. Show all work for full credit. 1, -3, -7, -11, ... (2 points)Application The table below shows the February balance of a simple interest savings account each year from 2015 to 2021 2015 2016 2018 2019 2020 2021 Balance $12,000 14018 16036 18054 20072 22090 24108 Do the balances form an arithmetic or geometric sequence? What is the d or the 1? Write a formula for the balance in the account n years after February 2015. Find the sum of the February balances from 2015 to 2032, inclusive. Find the error(s) and solve the problem correctly. Determine whether the sequence converges or diverges. How do you know if it converges or diverges? If it converges, give the limit. 5111 n+1 Answer: Diverges because of the degree of the numerator and denominator. Discussion Question Describe the difference between a recursive rule and an explicit rule when working with sequences