Question

What is the 33rd term of this arithmetic sequence? 12, 7, 2, -3, -8, …
a. -158
b. -157
c. -148
d. -147

Answer 1

$12,7,2,-3,-8,... \\ \\ a_1=12 \\ d=a_2-a_1=7-12=-5 \\ \\ a_n=a_1+d(n-1) \\ a_{33}=12-5(33-1) \\ a_{33}=12-5 \times 32 \\ a_{33}=12-160 \\ a_{33}=-148$

The answer is C.