finding next terms with recursive formula HELP PLEASE

Question

a sequence is defined by the recursive formula a₁ = -6 and a_n= a_n-1+2n. write out the next three terms of this sequence. show the work that leads to your answer.

Answer 1

This is easy, because you are given the starting term, -6. And you are given a formula a_n= a_n-1+2n.

So let's choose n = 2 so that we can calculate, from the formula, what a₂is.  The formula tells us that a₂ = a_2-1 + 2(2) which means -6 + 4 = -2.

 

Now repeat this, using n = 3, etc... Each term can be computed easily from the prior term--that's the meaning of the subscripts on the a's in the formula.