exam Maths Puzzle Numerical Ability

I can not figure this problem out could someone please help?

Find the term in the sequence: 1/2, -4, 32, _

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exam Other Question

The number of germs in a dish after t minutes is given as B=25e^(kt). If there are 2191 germs present after 6 minutes, find k (round out to 4 places). Let u and v be vectors in Rn, and let T be a linear operator on Rn. Prove that T(n).T(v)=n.v if and only if A(transpose)=A(inverse), where A is the standard matrix for T.