Write an explicit formula for the sequence -10, -7,-4,-1...?

Question

I need help understanding how to write explicit and recursive formulas

Answer 1

Jorden,

 

You can tell that each term is increasing by 3, and you know that the first time is -10.

 

So your common difference (d) is +3 and your initial term (a1) is -10.

 

Use the following formula:

 

a_n = a₁ + d(n -1)  --> so in this case --> a_n = -10 + 3(n-1)

 

This simplifies to a_n = 3n -13

If you substitute n = 1, 2, 3, and 4 (representing the position - 1st, 2nd, etc. of the term in the list) you get -10, -7, -4, -1