For each of the following recurrence relations write out

Question

Question: For each of the following recurrence relations, write out the first several terms of the sequence (at least five) and use this to find a closed form for the sequence. Then prove that each conjectured closed form is correct. (Is there a flashing sign in your head that indicates a fruitful approach?)

(a) a₁ = 3; a_n = 2a_{n - 1}

(b) a₁ = 4; a_n = 4 + a_{n - 1}

(c) a₁ = 1; a_n = 4 + a_{n - 1}