Question

Find the first term of the sequence 5,10,20,40, ... which exceeds 10.000

Answer 1

*10,000

Answer 2

\(10\times 2^k=10,000\) solve for \(k\)

Answer 3

The expression appears to be:
\[(2.5)2^n\]So we look for an \(n\) such that:
\[
(2.5)2^n>10000
\]Which is
\[
2^n>\frac{10000}{2.5}\implies \log_2(2^n)=n>\log_2(\frac{10000}{2.5})
\]