Which recursive formula generalizes the given sequence? 4, 12, 28, 60, 124, …

Question

it is multiple choice and uses a specific formula 

Answer 1

Check out:

1)   a₁ = 4

      a_n = 2a_n-1 + 4      for n > 1

 

b)   a₁ = 4

      a_n = a_n-1 + 2ⁿ⁺¹          for n > 1

 

. . .

 

If the choices don't include either of these, be sure that a₁=4, then calculate a₂, a₃, a₄, and a₅ recursively to check the formula.

Answer 2

a₁ = 4

a₂ = 12 = a₁ + 8 = a₁ + 2³

a₃ = 28 = a₂ + 16 = a₂ + 2⁴

a₄ = 60 = a₃ + 32 = a₃ + 2⁵

....

From the above pattern, the recursive formula for this sequence is

a₁ = 4

a_n = a_n-1 + 2ⁿ⁺¹ for n≥ 2

 

You did not provide the choices in your question. So the above answer may or may not match the choices available to you.