Step-by-step explanation:
We have to find the recursive formula that describes the correct sequence :
5, 13, 29, 61, 125,.....
Here, first no is 5 i.e. x₁ = 5, x₂ = 13, x₃ = 29, x₄ = 61 and x₅ = 125
If we multiply first number by 2 and adding with 3 we get :
x₂ = 2x₁ + 3 = 2 × 5 + 3 = 13
Similarly, x₃ = 2x₂ + 3 = 2 × 13 + 3 = 29
x₄ = 2x₃ + 3 = 2 × 29 + 3 = 61
and x₅ = 2x₄ + 3 = 2 × 61 + 3 = 125
So, the recursive formula is
. Hence, this is the required solution.