Create a recursion for the sequence an 3n 1SolutionGiven

Create a recursion for the sequence.

a_n = 3ⁿ + 1

Solution

Given : a_n = 3ⁿ + 1

then a_n+1 = 3ⁿ⁺¹ + 1

a_n+1 = 3ⁿ 3¹ + 1

a_n+1 = 3(3ⁿ ) + 1

a_n+1 = 3(3ⁿ + 1) - 3 + 1 (add and subtract 3)

a_n+1 = 3(a_n) - 2

That is its recursion : a_n+1 = 3(a_n) - 2