Question

What is the 33rd term for this arithmetic sequence... 12,7,2,-3,-8...

A.-158

B.-157

C.-148

D.-147

Answer 1

The difference between terms if -5, so


`a_n=a_(n-1)+(-5)=a_(n-2)+2\cdot(-5)=\cdots=a_1+(n-1)\cdot(-5)`


where
`a_1=12`, so


`a_(33)=12+(33-1)\cdot(-5)=-148`

making C the answer.