Question

Write the formula given the following arithmetic sequences.4, 2, 0, -2

Answer 1

so you know that the first term is 4 and the differences between the terms are -2. for every term you want to add the difference one time (in this case subtract 2), but since you have the first term, the second is the first term which applies the difference, so given n is the term number you add (n-1)*2 for every term. the arithmetic sequence is based on the first term, and we have that
\[a _{n}=a _{1}+(n-1)d=4+(n-1)(-2)=4-2n+2=6-2n\]