Let a₁, a2, a3, ... be the sequence defined recursively as follows. ak= 3ak-1 + 2 for each integer k ≥ 1 a₁ = 2 Use iteration to guess an explicit formula for the sequence by filling in the blanks below. Simplify the result by using a formula from Section 5.2. a₁ = 2 a2 = 3a1 + 2 2 = a3 аз = 3а2 + 2 3(3. ³() + = an = 3 a4 = 3a3 + 2 = 33 = 3 a5 = 3a4 + 2 = 3/3 = 3 = 3 ??? = 2 (3 = 3 = 2. 3 + 2 . + ??? ✓ ??? ✓ ??? V + 3. by definition of a ₁, 2, 3 ... +3. +3 2 + 3 +3 +3 3-1 Based on this pattern, it is reasonable to guess that ??? V ??? +3 ? V +2 ??? V 1 +2 + 2+3. by definition of a ₁, 2, 3, ... +3. +3 2 + 3 + 2 + 2 by definition of a ₁, 2, 3 ... 1' + +3. ++ 32 + 3 + 1) + 2 +2 by definition of a₁, a2, a3, ... 1' ·2+...+32.2+3·2+2 [by Theorem 5.2.2 with r = 3] for every integer n ≥ 1.