Question

Which recursive formula describes the sequence below? 5, 13, 29, 61, 125, ...

Answer 1

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 $x_n=2x_{n-1}+3$. Hence, this is the required solution.

Answer 2

(n x 2) + 3

5 x 2 = 10
10 + 3 = 13

13 x 2 = 26
26 + 3 = 29

and so on.