The remaining questions are about a recursively defined sequence Gn defined by G1 = 1, G2 = 3, and Gn = 2Gn-1 + Gn-2 for n 2 3. The next few values are G3 = 7 and G4 = 17. 3. Compute the sequence Gn through n = 10. 4. Prove that Gn is odd for every positive integer n. (Remember "strong" induction.) n 5. Prove that G2i-1 = (G2n - 1) for every positive integer n. i=1 6. Look at several examples of G? - Gn+1Gn-1 for n 2 2 and write out a careful, general conjecture. (You do not need to prove the conjecture.)