Question

What is the 9th term of the sequence 2, - 6, 18,- 54, ...?

a) 1,458
b)-4, 374
c) 13, 122
d)4,374

Answer 1

`a_1=2;\ a_2=-6;\ a_3=18;\ a_4=-54\\\\It's\ a\ geometric\ sequence:a_n=a_1r^(n-1)\\\\r=a_2:a_1\to r=-6:2=-3\\\\a_n=2\cdot(-3)^(n-1)\\\\n=9\to a_9=2\cdot(-3)^(9-1)=2\cdot(-3)^8=2\cdot6,561=13,122\\\\\boxed{a_9=13,122}`