Question

What is the general term equation, a_n , for the arithmetic sequence 5, 1,–3, –7…and what is the 21st term of this sequence?

Answer 1

The difference between each term is -4, so we know that part of the general term is -4n. Now we need to adjust -4n so at u1 it is 5. Therefore -4+x=5 and we rearrange to see x is 9.

Therefore our general sequence is:
$\boxed{u_n=-4n+9}$

Now we can substitute easily into the second equation with the common difference of 4:
$u_n=u_1+(n-1)d \\ u_{21}=5+(21-1)*-4 = 5-80 \\ \boxed{u_{21}=-75}$