Problem Solving

[Math Revolution GMAT math practice question]

If Sn=(Sn-1)^{-Sn-2}, S1=1, and S2=2, then S6=?

A. 1/2
B. 1/4
C. 2
D. 4
E. 16

find $$f_6$$
$$s_6=s\left(n-1\right)^{\left(-s_n-2\right)}$$
$$s_6=\frac{1}{s_5^{s_4}}$$
$$we\ \ need\ to\ find\ s_{5,\ }s_{4,\ }and\ s_3$$
$$s_3=\frac{1}{s_2^{s_1}}=\frac{1}{2^1}=\frac{1}{2}$$
$$s_4=\frac{1}{s_3^{s_2}}=\frac{1}{\left(\frac{1}{2}\right)^2}=1\cdot\left(\frac{2}{1}\right)^2$$
$$s_4=2^2=4$$
$$s_5=\frac{1}{s_4^{s_3}}=\frac{1}{4^{\left(\frac{1}{2}\right)}}=\frac{1}{\sqrt[]{4}}=\frac{1}{2}$$
$$s_6=\frac{1}{s_5^{s_4}}=\frac{1}{\left(\frac{1}{2}\right)^4}=1\cdot\left(\frac{2}{1}\right)^4$$
$$s_6=2^4=16$$
$$option\ E\ =\ answer$$

=>

S3=(S2)^-S1=(2)^-1=1/2
S4=(S3)^-S2=(1/2)^-2=4
S5=(S4)^-S3=(4)^-1/2=1/2
S6=(S5)^-S4=(1/2)^-4=16

Therefore, the answer is E.
Answer: E