Question

Which of the following is the formula for this geometric sequence?
1, -3, 9, -27,...
Answer

an = -1(3)n-1

an = 1(-3)n-1

an = 3(-1)n-1

Answer 1

An easy way is to just plug some values in for n and check to see which one works. The formula for any term in a geometric sequence is:\[a _{n}=a _{1}r ^{(n-1)}\] If you notice, the terms are being multiplied by -3 so r=-3. Also the first time is 1 so a1=1. Plug those values into the formula and you can get the answer without guess and check.