4. Consider the sequence defined recursively via: di 2, and d 2dn-1 +3 1, dn for all integers n 2 2. Prove by induction: for a integers n 5-2-1 3. 5. Consider the sequence defined recursively via: to 0, and tn tn-1 + 3n 1 for all integers n 21. Prove by induction: for all integers n 2 0, ra 6. Consider the sequence defined recursively via: eo = 2, and en len-1 +5 for all integers n 2 1. Prove by induction: for all integers n 2 0, en- 11-4h-5 3