Answer:
b. an = 2 • (-3)^(n - 1)
Step-by-step explanation:
Before we test a solution or two, we can easily discard most of them.
We see the values alternate of signs (-5 for the 2nd term and +162 for the 5th term)... so the progression factor has to be negative (in order to alternate sign). That already excludes answers A and C.
Normally, a geometric progression has the (n-1) exponent, not (n+1), so our chances seem to be better with B.
We can test both D and B with n = 2, to obtain -6
Let's test answer D before:
[tex]a_{2} = 2 * (-3)^{2+1} = 2 * (-3)^{3} = 2 * -27 = -54[/tex]
The result is -54, not -6... so it's not the right result.
Let's test answer B then:
[tex]a_{2} = 2 * (-3)^{2-1} = 2 * (-3)^{1} = 2 * -3 = -6[/tex]
Right! Let's verify with n=5 to get 162:
[tex]a_{5} = 2 * (-3)^{5-1} = 2 * (-3)^{4} = 2 * 81 = 162[/tex]
Confirmed, answer is B. an = 2 • (-3)^(n - 1)
